Question

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

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
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.
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.
A K-regular graph G is a graph such that deg(v) = K for all vertices v...
A K-regular graph G is a graph such that deg(v) = K for all vertices v in G. For example, c_9 is a 2-regular graph, because every vertex has degree 2. For some K greater than or equal to 2, neatly draw a simple K-regular graph that has a bridge. If it is impossible, prove why.
Suppose that a connected graph without loops or parallel edges has 11 vertices, each of degree...
Suppose that a connected graph without loops or parallel edges has 11 vertices, each of degree 6. a. Must the graph have an Euler Circuit? Explain b. Must the graph have a Hamilton Circuit? Explain c. If the graph does have an Euler Circuit, how many edges does the circuit contain? d. If the graph does have a Hamilton Circuit, what is its length?
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.
For each of the following, either draw a graph or explain why one does not exist:...
For each of the following, either draw a graph or explain why one does not exist: a) Circuit-free graph, 6 vertices, 4 edges b) Graph, 5 vertices, all of degree 3 c) Complete graph, 4 vertices, has an Euler circuit d) Complete graph, 4 vertices, has a Hamiltonian circuit
Prove or disapprove each of the following: (a) Every disconnected graph has an isolated vertex. (b)...
Prove or disapprove each of the following: (a) Every disconnected graph has an isolated vertex. (b) A graph is connected if and only if some vertex is connected to all other vertices. (c) If G is a simple, connected, Eulerian graph, with edges e, f that are incident to a common vertex, then G has an Eulerian circuit in which e and f appear consequently.
Supposed G is a graph, possibly not connected and u is a vertex of odd degree....
Supposed G is a graph, possibly not connected and u is a vertex of odd degree. Show that there is a path from u to another vertex v 6= u which also has odd degree.(hint: since u has odd degree it has paths to some other vertices. Just consider those.)
Supposed G is a graph, possibly not connected and u is a vertex of odd degree....
Supposed G is a graph, possibly not connected and u is a vertex of odd degree. Show that there is a path from u to another vertex v does not equal u which also has odd degree.(hint: since u has odd degree it has paths to some other vertices. Just consider those.)
GRAPH THEORY: Let G be a graph which can be decomposed into Hamilton cycles. Prove that...
GRAPH THEORY: Let G be a graph which can be decomposed into Hamilton cycles. Prove that G must be k-regular, and that k must be even. Prove that if G has an even number of vertices, then the edge chromatic number of G is Δ(G)=k.