Path of length 3 … and if there are three paths of length 4 before, there will be three paths of length 4 after. (d) Give an example of a path of length 5. Here, we study a rainbow version of their theorem, in which one considers graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. Apr 2, 2018 · Here's a hint: all paths from A to D will have to go through F. The length of a path is the number of edges it contains. Thinking of the problem this way, when we are counting paths of length three, we can think of this as counting the number of orders in which can traverse the four vertices. A path graph is therefore a graph that can be drawn so that all of its vertices and edges lie on a single straight line (Gross and Yellen 2006, p. (d) An x - z path of length 3. In the following weighted graph, the path b → a → c → d → e has total weight 1. Mar 5, 2018 · Problem: Draw a graph with $8$ vertices, all of odd degree, that doesn't contain a path of length $3$, or explain why such a graph doesn't exist. Let $C$ an odd cycle of smallest length (if any) in $G$. Is there a path of length 3 from vertex a to vertex c? If so, give an example. An old conjecture by Junger, Reinelt and Pulleyblank states that every 2-edge-connected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. We investigate a rainbow version of the A. If $v_0$ and $v_k$ are adjacent, you have a cycle of lenght $k+1$. We prove the Nov 1, 2017 · Let $v,w$ be two distinct vertices in the complete graph $K_n$, where $n \\geq 3$. kenneth rosen discrete mathematics Path: Let n be a nonnegative integer and G a directed graph. Find a cycle of length 8 in G . However, determining if there is HP, is NP Abstract. We investigate a rainbow version of the theorem, in which one considers k ≥ 1 graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. But going round the cycle, there's also a path of length 1, and going round multiple times, we nd paths of lengths 0; 1; 2, and so on. During this course of motion, the path length traversed is OP + PQ = + 360 m + (+120 m) = + 480 m. Average path length, the average number of steps along the shortest paths for all possible pairs of network nodes Hop count, the number of intermediate network devices through which data must pass between source and destination in a computer network Instruction path length, the number of machine code instructions required to execute a section of a computer program Discrete Math Exercise 4. 5 italic_δ. In a weighted graph, the length of a path is the sum of the weight of each of its edges. In a graph, there are no cyles of o der 0,1 Lemma 1. , this would imply K2 K 2 has two paths. d. A local path is structured in the following order: drive letter, colon, backslash, name components separated by backslashes, and a terminating null character. This MATLAB function returns the total length of path by summing the distances between every sequential pair of states in the path. (e) An x - t path of length d (x, t). Give an example of a path of length 5 Is there a path of length 3 from vertex d to vertex f? If so, give an example. Andrzej Grzesik Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland. 5 = 12. To compute a path of length 2, the matrix of length 1 must be multiplied by itself, and the product matrix is the matrix representation of path of length 2. Here’s the best way to solve it. It's important to note that the graph structure is not provided here, so let's assume a common structure where vertices a, Show more… Jan 13, 2013 · In a graph $G$ all vertices have degrees $\le 3$. Download scientific diagram | A path of length 3 a cycle of length 3. Which of the following is NOT a path of length 3 from V1 to V2 in this digraph? V1⋯V1⋯V3⋯V2V1⋯V2⋯V3⋯V2V1⋯V3⋯V3⋯V2V1⋯V3⋯V2⋯V2V1→V2⋯V1⋯V2 Show transcribed image text For small 𝑔 g italic_g we obtain better bounds, e. The length of a path is the number n of edges in that path. You must select all of the true statements to get full credit for this question. Draw the subgraphs G - X and G-U of G Figure 1. b) consider a path $v_0\dots v_k$ of length $k$ (existing for part a) and for Chandru's construction) such that $v_i \neq v_j$ $\forall i\neq j$. We can also describe a path as a sequence of the k 1 edges fv0; v1g; : : : ; fv` 1; v`g. Learning Objectives Determine the length of a particle’s path in space by using the arc-length function. $P_4$ must mean a $4$-vertex path (a path of length $3$), otherwise the claim is not true; the $5$-vertex cycle is a counter-example. path is a global variable. Apr 21, 2018 · I thought "length" referred to the number of vertices, but I think if you now look at $v_1v_6$, you can show (using planarity this time) that there must be a path of length $6$. Oct 29, 2015 · Hm, although with that definition of "path", there isn't a path of length $4$ between all the vertices. If a, b, c belong to the same block B ∈ B, then let B = {a, b, c 18 'Length' of a path is the number of edges in the path. In other words, paths in the graph are invariants. Nov 9, 2016 · So $v_1$ would not appear twice in a path (we would call that a cycle), but you'd have to name the edges to define a path. Is (d, b, c, g,c, f, e, c, d) a circuit in the graph? Is it a cycle? What is the longest cycle in the graph? Give an example of a cycle of length 4. We prove the Sep 30, 2019 · We determine f (n, H) exactly in the case when H is a path of length 3. If you have a path of length n, in a graph containing n nodes, and can visit each node at most once - you have Hamiltonian Path (HP). 1974). So, total paths must be $\binom {4} {2} \times 2=12$ But the answer is given to be 2. This can account for cycles - it takes into account ALL paths of a given length. We determine f(n, H) exactly in the case when H is a path of length 3. Math Advanced Math Advanced Math questions and answers For the graph G of Figure 1. 3. Oct 27, 2019 · here Path: A path in a graph is a subgraph of a given graph that is isomorphic to a path graph. Specific types of path lengths known as the external path length and internal path length are defined for extended binary trees. (g) A cycle of length 8. Show that G contains a cycle of length at least k. Jul 12, 2025 · Time Complexity - Since we have to multiply the adjacency matrix log (k) times (using matrix exponentiation), the time complexity of the algorithm is O ( (|V|^3)*log (k)), where V is the number of vertices, and k is the length of the path. 1. (b) A v-w trail that is not a v- w path. g. Then $v$ has at least 3 neighbors on $P$. A maximal planar graph with 9 vertices, containing maximum number of 3-paths. Draw a graph with 8 vertices, all of odd degree, that does not contain a path of length 3 or explain why such a graph does not exist. Since, path of length 2 would have 3 vertices, So selecting 2 terminal vertices of a path in $\binom {4} {2}$. Nov 27, 2024 · Continue reading to learn more about the Path of Exile 2 campaign length and figure out how long it will take to beat. A path from u to v is a shortest path if there is no shorter path from u to v. 1 + 4. In a social network's graph, a path of length n means you know this person through n − 1 connections. See Answer Question: Consider the digraph. Let $x$, $y$, $z$ be 3 such neighbors of $v$ in order on $P$. Another e. 12 1. The following argument is divided into two cases. Solution: Let $P$ be a maximal path in $G$ with $v$ is an endpoint of $P$. 20). Apr 16, 2024 · Find the number of paths of length n between any two adjacent vertices in K 3,3 for the values of n = 2,3,4,5. We prove the Oct 12, 2023 · Solution For A person moves on a rectangular path of length 3 m \\& breadth 4 m, then find the ratio of distance \\& displacement when it reaches at dia Online application to ascertain the sun movement with interactive map, sunrise, sunset, shadow length, solar eclipse, sun position, sun phase, sun height, sun calculator, solar eclipse, elevation, Photovoltaic system, Photovoltaic This entry represents a path of length 1 from v i to v j. How would you discover how many paths of arbitrary length n link any two nodes? Apr 19, 2016 · 3 First, I'm going to presume that by path, you want to exclude loops. (c) An r - z path of length 2. 3 (b) is complete but not full. If there is a path of length 3 from a to b, then after the isomorphism is applied, there will be a path of length 3 from f(a) to f(b). Fans of western style cultivation fantasy, post apocalypse and Xianxia will enjoy. 2) Prove that in a graph, any walk that starts and ends with the same vertex and has the smallest possible non-zero length, must be a cycle. The (ij)th entry of the path length matrix is the length of the shortest path from vertex vi to vertex vj; if there is no path between these vertices, then the value of the entry is 1. ) If there exists Sep 28, 2022 · D to F to D to C has length 3. Is it a mistake? Newman's book Jan 7, 2013 · I have a problem with the following assignment. Describe all graphs which do not contain a path whose length 3. Jun 14, 2025 · Last update: June 14, 2025 Translated From: e-maxx. The shortest-path problem is ill-posed in graphs with negative cycles. Consider 3 $v$, $y$-paths: the edge $vy$; the edge $vx$ followed by the $x$, $y$-path in $P$; and the edge $vz$ followed by the $z$, $y$-path in $P$. e. Typically a path is considered to be undirected. Find a directed path of length 2 from B to C. Dec 22, 2018 · My work. Give an 6 days ago · The path graph P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2. 2 + 3. a) (Node Repeated Paths): There are 6 paths of length 3 from P to Q (and vice versa) with Sep 30, 2019 · The function f(n, H) has been determined when H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. Nov 13, 2025 · Path of Exile is a free online-only action RPG under development by Grinding Gear Games in New Zealand. [4] The girth of a graph is the length of its shortest cycle, but this cycle [page 30, #3 ] Let G be a graph containing a cycle C, and assume that G contains a path of length p at least k between two vertices of C. The induced path number of a graph G is the smallest number of induced paths into which the vertices of the graph may be partitioned, [3] and the closely related path cover number of G is the smallest number of induced paths that together include all vertices of G. uj. LinkedIn actually shows you these paths: I am a “2nd degree contact” when there is a path of length Sep 13, 2024 · The reason behind this is quite simple, because we search for all possible path of length (n-1) = 3 using these 2 vertices which include the remaining 3 vertices. For example: <1,2,3,4,5,6,7,8,9,10> Find cycles of length 5, 6, 8 A path of length 3 between vertices a and c means we are looking for all possible ways to go from vertex a to vertex c with exactly 3 edges. The function f (n, H) has been determined when H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. The path graph of length n is implemented in the Wolfram Language as PathGraph[Range[n]], and precomputed properties of path graphs are You mast select all of the true statements to get full credic for this question. I have a friend X and they know Y. Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. for 𝑔 3 g=3 italic_g = 3 we show that oriented graph with minimum out-degree 𝛿 \delta italic_δ contains a directed path of length 1. In most contexts, a path must contain at least one edge, though in some applications (e. Quiz #17 SOLUTIONS f 10 points g Find the number of paths of length 3 between two di erent vertices in K4. May 27, 2022 · Having picked $x_1y_1$ then you pick $x_2$ uniformly at random from the neighbours of $y_1$, and having picked $x_2$ you pick $y_2$ uniformly at random from the neighbors of $x_2$. Here we study a rainbow version of their theorem, in which one considers k ≥ 1 graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. (e) Is there a path of length 3 from vertex d to vertex f? If so, give an example Dec 10, 2009 · Maximum Path Length Limitation In the Windows API (with some exceptions discussed in the following paragraphs), the maximum length for a path is MAX_PATH, which is defined as 260 characters. Problem did not say illegal for path to use same node twice. BEDAB is a circuit of length 5 . Given a source and a destination vertex, I want to find the number of paths form the source vertex to the destination vertex of given length k. OB. The number ` is the length of the path. Let the vertices of the graph are v1, v2, v3, and v4. For example: <1,2,3,4,5,6> Find a path of length 9. Nov 12, 2025 · The length of a graph path is the number of edges it contains. Could you help me solve it? The actual problem is a lot more complex with constraints for certain nodes (how many times you can visit it, rules against visiting it if a certain sequence of nodes were hit prior, etc. In 1959 Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. Let P denote the 3-uniform path of length three by which we mean the only connected 3-uniform hypergraph on seven vertices with the degree sequence (2; 2; 1; 1; 1; 1; 1). 2: Directed graph definitions, cont. A path in a graph G is a subgraph of G that is a path graph (West 2000, p. A circuit is a walk from a ertex v to v. This is one less than the number of vertices from the beginning of the first edge to the end of the last edge, inclusive. So, these 2 vertices cover the cycles of remaining 3 vertices as well, and using only 3 vertices we can't form a cycle of length 4 anyways. 5\delta 1. Describe the meaning of the normal and binormal vectors of a curve in space. A directed path of length 2 from B to C is B. Thus, the answer will need to be divided by 2 2 (since each undirected path is counted twice). The vertices v0 and v` are the endpoints of the path. e. Download scientific diagram | Path of length 3 with a path of length two from publication: Maximum Cardinality Neighbourly Sets in Quadrilateral Free Graphs | Neighbourly set of a graph is a Jun 27, 2019 · Yeah all_pairs_dijsktra_path_length would do the trick if I want to find out how many paths in graph have length of 3 or lower, but I would like to get the sum of weights of the edges in the path and only for paths with length of 3 not lower. a) Find the vertex matrix M of the following graph. Example: Consider the following graph. Feb 17, 2014 · Here, k is the length of the path and routes [] [] is the adjacency matrix of the graph. Mar 6, 2018 · Suppose to have a graph, represented through its adjacency matrix. Jan 1, 2023 · In 1959 Erd\H os and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. What am I missing? UPDATE: I am attaching a snapshot of Newman's book. path: a trail with no repeated vertices (except possibly the initial and final vertex). Path of Exile is a free online-only action RPG under development by Grinding Gear Games in New Zealand. Math Advanced Math Advanced Math questions and answers Draw a graph with 8 vertices, all of odd degree, that does not contain a path of length 3 or explain why such a graph does not exist. The diagram below shows a directed graph. What is the degree of vertex 8? What is the degree of vertex 10? How many vertices of degree 2 are there in G? List them. CAT 2020 slot 3 Question 63|| Anil, sunil and ravi run along a circular path of length 3 km Sandeep Garg Sir - Quantitative Aptitude 1. (b) A v - w trail that is not a v - w path. So you can ask how many paths there are from A to F, and how many there are from F to D, and you can match up their lengths. An s,t-path is a path whose This paper proposes to study properties of a graph G by also using the path length matrix for the graph. How many walks of length 3 are there from $v$ to $w$? It is explained as follows All possible types of paths of length 3, from different structures contributing to the term [e T A 3 e]. Explain why your answer is correct. For example… In the digraphs of relations, a path of length n from a to b meant that (a, b) was in Rn. AAC is a path of length 3 , ADEE B is path of length 4. ABC is a path of length 3, ADEEB is path of length 4. What is the length of a shortest path from 3 to 4? What is the length of a shortest path from 8 to 7? Find a path of length 5 from vertex 4 to vertex 6 . 1 There is no particular relationship between these two tree shapes; that is, the tree of Figure 6. one divides the domain of the path into a finite number of segments $$ -\pi = t_0 < t_1 < t_2 < t_3 < \dots < t_ {n-1} < t_n = \pi $$ and approximates the length of each segment of the path by the length of the velocity vector at the left end point of each segment of the domain. We also present a 2-edge-connected non-planar graph that can be embedded on the torus and Aug 2, 2024 · Path of the Berserker Book 3 is a progression fantasy novel that contains immortal cultivators, an oppressive intergalactic dynasty, rage-inducing imperial bureaucracy, magical spirit beasts, fantastical martial arts and one pissed off MC who’s sick of it all. First, as you said "Your path can be anywhere between length 3 and length n", what about those paths that are u -> v -> w as those have length 2, or is since there is only 1 of those (directly from u to v to w) that is just one choice? Our expert help has broken down your problem into an easy-to-learn solution you can count on. a rainbow version of the theorem, in which one considers k 1 graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in Sep 14, 2022 · Figure 6. (a) Is ⟨d, b, c, g, c, f, e, c, d⟩ a circuit in the graph? Is it a cycle? (b) What is the longest cycle in the graph? (c) Give an example of a cycle of length 4. In the Petersen graph, there are several trails of length 5. A directed path (sometimes called dipath[1]) in a directed graph is a In the following directed graph The sequence 4 → 3 → 2 → 1 is a path of length 3, while 5 → 3 → 2 → 1 is not a path. The length of a path is the number of traversed edges. Nov 1, 2023 · In the given scenario, a person moves along a rectangular path of length 3 m and breadth 4 m, reaching a diagonally opposite point. OA. 4) Prove by induction that if every Apr 19, 2022 · The function f (n, H) has been determined when H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. We determine f (n, H) exactly in the case when H is a path of length 3. When calculating path length in one-dimensional motion, like running back and forth on a straight track, you simply add up all the distances you’ve covered, even if you’ve retraced your steps. Dec 9, 2024 · When it comes to the question of how long it takes to beat Path of Exile 2, length ultimately depends on your skill, luck, and how far you want to go. , the path of length 2 2 from vertex 1 1 to vertex 3 3 is considered different to the path of length 2 2 from vertex 3 3 to vertex 1 1. E-mail: Sebastian. 3 + 3. A directed path of length 3 from B to Eis BCDE. $v_1v_2$ would equal $v_2v_1$ since it is the same edge. (f) Is there a path of length 3 from vertex a to vertex c? If Apr 14, 2014 · In a complete graph of N nodes, the number of k-length paths from node A to B is (N-2)*(N-3)^(k-2) (assuming no self-edges, nodes A and B can only appear as endpoints of the path, and k > 1). 3 (a) is full but not complete while the tree of Figure 6. There is no solution. (b) Find 2 cycles of length 5 for the graph in part (a). (d) An a -z path of length 3. Babinski@alumni. (c) Find a walk of length 3 that is neither a path nor a cycle. The heap data structure is an example of a complete binary tree. 20, give an example of each of the following or explain why no such example exists (a) An a -y walk of length 6. , defining the path covering number), "degenerate" paths of length 0 consisting of a single vertex are allowed (Boesch et al. (b) Find a cycle of length 3. Nov 4, 2022 · In 1959 Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. It can be proved that if M is the vertex matrix of a digraph, then the entry will show the number of r-step connections from to . 5 𝛿 1. We prove the conjecture for a class of planar graphs including all 2-edge-connected series-parallel graphs. Show that we can color its vertices in two colors so that in $G$ there exists no one-color path, whose length is $3$. I am connected to Y by a path of length 2. i. 18). ABCA is circuit of length 3. We can visit each vertex as many times as we want, so if a path from a to b goes like this: a -> c -> b -> c -> b it is considered valid. (For instance, if you want a total path of length 6, then you can only match up a path from A to F of length 4 with a path from F to D of length 2, as 4 + 2 = 6. Question: Which of the following statements are true about the graph below? There may be more than one true statement. trail: an alternating sequence of vertices and edges with no repeated edges. ABCA is circuit of length 3 . Suppose this path contains a circuit starting and en ing with, say, vi. There's this quite popular lemma that if in a graph all vertices have degrees $\ge d$, then in this graph there's a path whose length is $d$. Select the correct choice below and fill in any answer boxes in your choice. Find a trail of length 5. Keep reading to discover how long it might take to finish the main story, reach max level, and explore the length of each act. A path in G is a sequence v 0 → e 1 v 1 → e 2 → e n v n, where the v k are distinct vertices in G and e k is an edge in G from v k 1 to v k. That is, we are picking the number of ways to permute the vertices. (a) An x - y walk of length 6. [there's another length 3 path from D to C] In this paper we determine f( n, P4), the maximum number of copies of a path of length three possible in n-vertex planar graph. This circuit must use at least one edge of the path; hence, after removing the circuit we will have a path from u to v of length < n, contradicting the minimality o Graphs without a rainbow path of length 3 † Sebastian Babiński Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland. 11 and 1. Aug 13, 2016 · Does it mean that there are 6 paths of length 3 from vertex-2 to vertex-1? Cearly it is not true because I have only $1$ path of length $3$ from 2 to 1, namely the sequence: $ (2,4,5,1)$. So I suppose the question actually means "walk" rather than "path". If it does not repeat any vertices other than v, and is of length two or more, then it is a cycle of order n where n is the lengt of the walk. Aug 24, 2021 · Let f (n, H) denote the maximum number of copies of H possible in an n -vertex planar graph. A graph's adjacency matrix can tell us a lot about its paths. Displacement It is useful to define another quantity displacement as the change in position. He only talks about "paths", but never about a "walk". The total distance travelled is the sum of the lengths of the two sides of the rectangle, which is 3 m + 4 m = 7 m. What mistake I did? You must select all of the true statements to get full credit for this question. ) In the case of your final graph, there's a For the case d = ω(n1/2 ≥ log n), Lemma 2. 12 For the graph G of Figure 1. Path Length is always positive or zero; it never decreases. Our main result is the following. Number of paths of a fixed length We are Nov 21, 2024 · On average, completing Path of Exile 2's (PoE 2) main campaign is expected to take around 40-50 hours. 1 Paths and cycles A path in a graph is a sequence of distinct vertices v0; : : : ; v` such that fvi; vi+1g is an edge in the graph for all 0 i < `. ABCA is circuit of length 3. 1 implies that whp there exists an induced path even of the asymptotically optimal length Split the vertex set [n] into V1 and V2 each of size at least n/3. (The de nition allows for paths of length zero. This guarantees that $x_1y_1x_2y_2$ is a path of length $3$ (possibly with repeated vertices, as we need for the statement of Sidorenko's conjecture). In 1959, Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. Explain the meaning of the curvature of a curve in space and state its formula. (e) Is there a path of length 3 from vertex d to vertex f? If so, give an example. n G of length < n. (f) A circuit of length 10. ru Number of paths of fixed length / Shortest paths of fixed length The following article describes solutions to these two problems built on the same idea: reduce the problem to the construction of matrix and compute the solution with the usual matrix multiplication or with a modified multiplication. 3 illustrates the differences between full and complete binary trees. t not a path. 20, give an example of each of the following or explain why no such example exists. 20: The graph G in Exercises 1. The possible paths between two of them, say v1 and v4 are: v1 7!v2 7!v1 7!v4 v1 7!v2 7!v3 7!v4 Get your coupon Math Other Math Other Math questions and answers (a) Find a path of length 3 from the vertex v2 to the vertex 05. b) Find the number of 3 step connection (or paths of length 3) from to . In a graph, if there is a walk from v to w then there is a path from v to w. We prove the Jul 7, 2021 · Exercise 12 3 1 1) In the graph (a) Find a path of length 3. My approach What is a path of length $3$? $\impli E. c) Find the number of 1, 2 or 3-step connections The diagram below shows a directed graph. Math Advanced Math Advanced Math questions and answers 2. 3) Prove Proposition 12. And now 1 vertex needs to be selected, which can be done in 2 ways. ) makes the problem NP-Hard. Again, there are several. pl. 17K subscribers Subscribe. 2. Example: Computing A Matrix Representation of Path of Length 2 g This is not a path since it is disconnected and also d appears multiple times. (c) An r- z path of length 2. And a similar one. Definition 3. Case 1. edu. A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). Path length is a scalar quantity — a quantity that has a magnitude only and no direction (see Chapter 4). ABC is a path of length 3 ,ADEEB is path aflength 4. (h) A Dec 9, 2024 · How Long Is Path Of Exile 2: Campaign Length And Quest List Path of Exile 2 might only be in early access, but there are hours of content and dozens of quests to dive into. They run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively. For example, there are two shortest paths from f to e above. Question: For each nonnegative integer n, determine the maximum possible number of edgesin any graph with n vertices which has no clique of size 3 and no path of length 3. iuwui mys bjhg qekb brmst dycpg hrdmmnt xav wckius rvntwg xrmb ibufr pfom cdxto sihjaxn