Question

(a) Show that the chromatic number of the Petersen graph is exactly 3. (b) Find the...

(a) Show that the chromatic number of the Petersen graph is exactly 3.

(b) Find the chromatic number of the k-cube Qk for any k, and of Kn−e where n ≥ 3 and e is any edge

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that a graph G has chromatic number less than or equal to n if and...
Show that a graph G has chromatic number less than or equal to n if and only if there is a graph morphism (cf. PS 4) f : G → Kn, where Kn is the complete graph on n vertices.
Graph Theory, discrete math question: Let G be a graph with 100 vertices, and chromatic number...
Graph Theory, discrete math question: Let G be a graph with 100 vertices, and chromatic number 99. Prove a lower bound for the clique number of G. Any lower bound will do, but try to make it as large as you can. Please follow this hint my professor gave and show your work, Thank you!! Hint: can you prove that the clique number is at least 1? Now how about 2? Can you prove that the clique number must be...
Show that there is only one graph whose chromatic polynomial is ?5 −4?4 + 5?3 −2?2....
Show that there is only one graph whose chromatic polynomial is ?5 −4?4 + 5?3 −2?2. (Graph Theory)
Discrete math, graph theory question: Let G be a graph with 100 vertices, and chromatic number...
Discrete math, graph theory question: Let G be a graph with 100 vertices, and chromatic number 99. Prove a lower bound for the clique number of G. (Hint: Any lower bound will do, but try to make it as large as you can.)
Let G be a simple graph having at least one edge, and let L(G) be its...
Let G be a simple graph having at least one edge, and let L(G) be its line graph. (a) Show that χ0(G) = χ(L(G)). (b) Assume that the highest vertex degree in G is 3. Using the above, show Vizing’s Theorem for G. You may use any theorem from class involving the chromatic number, but no theorem involving the chromatic index
A graph G is said to be k-critical if ?(?)=? and the deletion of any vertex...
A graph G is said to be k-critical if ?(?)=? and the deletion of any vertex yields a graph of smaller chromatic number. (i) Find all 2-critical and 3-critical simple graphs. Be sure to justify your answer.
Proof: Let G be a k-connected k-regular graph. Show that, for any edge e, G has...
Proof: Let G be a k-connected k-regular graph. Show that, for any edge e, G has a perfect matching M such that e ε M. Please show full detailed proof. Thank you in advance!
a. A graph is called k-regular if every vertex has degree k. Explain why any k-regular...
a. A graph is called k-regular if every vertex has degree k. Explain why any k-regular graph with 11 vertices must conain an Euler circuit. (Hint – think of the possible values of k). b. If G is a 6-regular graph, what is the chromatic number of G? Must it be 6? Explain
Q. a graph is called k-planar if every vertex has degree k. (a) Explain why any...
Q. a graph is called k-planar if every vertex has degree k. (a) Explain why any k-regular graph with 11 vertices should contain an Euler’s circuit. (what are the possible values of k). (b) Suppose G is a 6-regular graph. Must the chromatic number of G be at leat 6? Explain.
Show that an edge e of a connected graph G belongs to any spanning tree of...
Show that an edge e of a connected graph G belongs to any spanning tree of G if and only if e is a bridge of G. Show that e does not belong to any spanning tree if and only if e is a loop of G.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT