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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.

  1. Prove that G must be k-regular, and that k must be even.

  2. Prove that if G has an even number of vertices, then the edge chromatic number of G is Δ(G)=k.

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