Question: If every vertex in a graph G has degree d, then show that G must contain a circuit of length at least d + 1.

If every vertex in a graph G has degree d, then show that G must contain acircuit of length at least d + 1.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

The following trial balance of Sergei Asbrecht Co. does not balance. Each of the listed accounts has a normal balance per the general ledger. An examination of the ledger and journal reveals the...

Q:

a) Give a counterexample to the claim in the Theorem. b) Identify the mistake in the "proof."

Q:

#2, MATH3825/MATH3855/COMP3805, Winter 2017 Due on 24 March. Total: 100 marks 1. [10 marks] You are building a wall out of Lego bricks. You have bricks of length 1 and bricks of length 2. Let bn be...

Q:

discrete structures Problem 2. (10 points) Let G = (V,E) be a graph for which each vertex is colored either black or white (but not both). We say that vertex v is integrated if at least half of its...

Q:

Problem 2. (10 points) Let G = (V,E) be a graph for which each vertex is colored either black or white (but not both). We say that vertex v is integrated if at least half of its neighbors (those...

Q:

Problem 2. (10 points) Let G = (V,E) be a graph for which each vertex is colored either black or white (but not both). We say that vertex v is integrated if at least half of its neighbors (those...

Q:

2.A Dominating Set of a graph is a collection of vertices which cover every vertex not in that collection i.e. every vertex not in the collection is connected to at least one vertex in the...

Q:

The clique problem can be stated as follows: Given an undirected graph G = (V, E) and an integer K, does G contain a complete subgraph of at least K vertices? The vertex cover problem can be stated...

Q:

For each decision problem D below, state whether D e P or D E NP, then justify your claim For decision problems in P, describe an algorithm that decides the problem in polytime (including a brief...

Q:

4. Let G = (V,E) be a loop-free graph. Its line graph L(G) is the graph defined as follows: the vertex set of L(G) is in one-to-one correspondence with the set of edges of G and two vertices of L(G)...

Q:

(a) A simple connected undirected graph is regular if every vertex of the graph has the same degree. LetAGdenote the adjacency matrix of a simple undi- rected graphG. Determine in terms of the...

Q:

Three blocks with masses m1 = 5.00 kg, m2 = 10.0 kg, and m3 = 15.0 kg are connected by massless strings which run over two frictionless pulleys. Block 1 sits on a highly polished plane inclined at an...

Q:

Please describe this formula which is about calculating interest rates at different compounding frequencies m R = (1 + )" - 1 m

Q:

Ia an attempt to lower its preduction cents, a firm relocates some of its manufacturing facilities to China, which has much lower labor cost. The firm uses which of the following strategies?...

Q:

On December 31, 2020, Dow Steel Corporation had 800,000 shares of common stock and 320,000 shares of 8%, noncumulative, nonconvertible preferred stock issued and outstanding. Dow issued a 4% common...