Question

A graph is k-colorable if each vertex can be assigned one of k colors so that...

A graph is k-colorable if each vertex can be assigned one of k colors so that no two adjacent vertices have the same color. Show that a graph with maximum degree at most r is (r + 1)-colorable.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose we are going to color the vertices of a connected planar simple graph such that...
Suppose we are going to color the vertices of a connected planar simple graph such that no two adjacent vertices are with the same color. (a) Prove that if G is a connected planar simple graph, then G has a vertex of degree at most five. (b) Prove that every connected planar simple graph can be colored using six or fewer colors.
a graph is regular of degree k if every vertex has the same degree, k. show...
a graph is regular of degree k if every vertex has the same degree, k. show that G has a hamiltonian circuit if G has 13 vertices and is regular of degree 6.
Let G be a simple graph in which all vertices have degree four. Prove that it...
Let G be a simple graph in which all vertices have degree four. Prove that it is possible to color the edges of G orange or blue so that each vertex is adjacent to two orange edges and two blue edges. Hint: The graph G has a closed Eulerian walk. Walk along it and color the edges alternately orange and blue.
Graph Theory: What is the maximum degree a vertex can have in a tree graph with...
Graph Theory: What is the maximum degree a vertex can have in a tree graph with 3 leaves.
Let n be a positive integer, and let Hn denote the graph whose vertex set is...
Let n be a positive integer, and let Hn denote the graph whose vertex set is the set of all n-tuples with coordinates in {0, 1}, such that vertices u and v are adjacent if and only if they differ in one position. For example, if n = 3, then (0, 0, 1) and (0, 1, 1) are adjacent, but (0, 0, 0) and (0, 1, 1) are not. Answer the following with brief justification (formal proofs not necessary): a....
You are given a directed acyclic graph G(V,E), where each vertex v that has in-degree 0...
You are given a directed acyclic graph G(V,E), where each vertex v that has in-degree 0 has a value value(v) associated with it. For every other vertex u in V, define Pred(u) to be the set of vertices that have incoming edges to u. We now define value(u) = ?v∈P red(u) value(v). Design an O(n + m) time algorithm to compute value(u) for all vertices u where n denotes the number of vertices and m denotes the number of edges...
Can you construct a graph on 100 vertices where no two of these 100 vertices have...
Can you construct a graph on 100 vertices where no two of these 100 vertices have the same degree?
please solve step by step. thank you A bipartite graph is a graph whose vertices can...
please solve step by step. thank you A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Show that a simple graph is bipartite if and only if it is 2-colorable.
Question 38 A simple connected graph with 7 vertices has 3 vertices of degree 1, 3...
Question 38 A simple connected graph with 7 vertices has 3 vertices of degree 1, 3 vertices of degree 2 and 1 vertex of degree 3. How many edges does the graph have? Question 29 Use two of the following sets for each part below. Let X = {a, b, c}, Y = {1, 2, 3, 4} and Z = {s, t}. a) Using ordered pairs define a function that is one-to-one but not onto. b) Using ordered pairs define...
Three point charges are arranged so that they each lie on the vertex of what appears...
Three point charges are arranged so that they each lie on the vertex of what appears to be an equilateral triangle of side length 1 cm. At the bottom, the two charges are the same (from left to right), each having charge +10 nC (nanoCoulomb). At the vertex on the top, the charge there is (-)20 nC (it's a negative charge). Find the magnitude and direction of the net electric force on the top charge due to the bottom two.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT