Question: This is part c) A-9-4. {5 marks} Let G = (V, E) be a graph, and suppose that a maximum matching M of G contains

This is part c)

A-9-4. {5 marks} Let G = (V, E) be a graph, and suppose that a maximum matching M of G contains m edges. (a) Prove that G can be coloured with 2m + 1 colours. (b) Prove that if G is connected and has an even number of vertices, then G can be coloured with 2m colours. (c) Give examples which show that the number of colours in the previous parts cannot be decreased

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