Question

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.

Answer #1

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

a
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