3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...

Question

Question

3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that there exist two vertices s and t

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Guven and destrnatponE, no.of & da e dlinJorm de dlistoint they dont shue any eslge Sowreo exs can be mapeimum two eage disj The problenp can be solved by reduelg Houo problem it k maimom foll ovotnq are D Consider the aven Souw ca and destinadfon as

Add a comment

Answer 2

Similar Homework Help Questions

Exercise 5. Let G be a graph in which every vertex has degree at least m....

Exercise 5. Let G be a graph in which every vertex has degree at least m. Prove that there is a simple path (i.e. no repeated vertices) in G of length m.
Let G = (V;E) be an undirected and unweighted graph. Let S be a subset of the vertices. The graph...

Let G = (V;E) be an undirected and unweighted graph. Let S be a subset of the vertices. The graph induced on S, denoted G[S] is a graph that has vertex set S and an edge between two vertices u, v that is an element of S provided that {u,v} is an edge of G. A subset K of V is called a killer set of G if the deletion of K kills all the edges of G, that is...
Question 1: Given an undirected connected graph so that every edge belongs to at least one...

Question 1: Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Question 2: Given a graph G(V, E) a set I is an independent set if for every uv el, u #v, uv & E. A Matching is a collection of edges {ei} so...

B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V → {0, 1, . . . ,k-1}

B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V → {0, 1, . . . ,k-1} such that c(u)≠c(v) for every edge (u, v) ∈ E. In other words, the numbers 0.1,... k-1 represent the k colors, and adjacent vertices different colors. must havec. Let d be the maximum degree of any vertex in a graph G. Prove that we can color G with d +1 colors.
2) Let G ME) be an undirected Graph. A node cover of G is a subset...

2) Let G ME) be an undirected Graph. A node cover of G is a subset U of the vertex set V such that every edge in E is incident to at least one vertex in U. A minimum node cover MNC) is one with the lowest number of vertices. For example {1,3,5,6is a node cover for the following graph, but 2,3,5} is a min node cover Consider the following Greedy algorithm for this problem: Algorithm NodeCover (V,E) Uempty While...
Bounds on the number of edges in a graph. (a) Let G be an undirected graph...

Bounds on the number of edges in a graph. (a) Let G be an undirected graph with n vertices. Let Δ(G) be the maximum degree of any vertex in G, δ(G) be the minimum degree of any vertex in G, and m be the number of edges in G. Prove that δ(G)n2≤m≤Δ(G)n2

Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and...

need help with a and b in this graph theory question Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and connecting each vertex to the exact a) Show that for all u,v there are k internally disjoint u, v-paths (you (b) Use the previous part, even if you did not prove it, to show that the e vertex and the k 1 closest vertices on either...
Prove that, if G is a nontrivial connected graph in which every vertex has even degree, then the ...

Prove that, if G is a nontrivial connected graph in which every vertex has even degree, then the edge connectivity of G is no less than 2. Prove that, if G is a nontrivial connected graph in which every vertex has even degree, then the edge connectivity of G is no less than 2.
Let G= (V, E) be a connected undirected graph and let v be a vertex in...

Let G= (V, E) be a connected undirected graph and let v be a vertex in G. Let T be the depth-first search tree of G starting from v, and let U be the breadth-first search tree of G starting from v. Prove that the height of T is at least as great as the height of U

Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...

Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...

3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...

Homework Answers

Add Answer to:
3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...

Post as a guest

Earn Coins

Exercise 5. Let G be a graph in which every vertex has degree at least m....

Let G = (V;E) be an undirected and unweighted graph. Let S be a subset of the vertices. The graph...

Question 1: Given an undirected connected graph so that every edge belongs to at least one...

B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V → {0, 1, . . . ,k-1}

2) Let G ME) be an undirected Graph. A node cover of G is a subset...

Bounds on the number of edges in a graph. (a) Let G be an undirected graph...

Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and...

Prove that, if G is a nontrivial connected graph in which every vertex has even degree, then the ...

Let G= (V, E) be a connected undirected graph and let v be a vertex in...

Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...

3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...

Homework Answers

Add Answer to: 3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...

Post as a guest

Earn Coins

Add Answer to:
3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...