If you say minimum then it should be 2 ( a cyclic graph with even vertices required 2 colours and for odd 3 ) and we can form a cyclic graph with 4 vertices and 5th vertex will connect any one of that cyclic vertices with one edge (of course :D ) . peace
if it a null graph then only 1 colour is needed .
Hi @Pranay Datta 1
@Arjun sir
Can you please explain this logic ? Because I knew C_{5 }or any odd vertices cycle graph is 3 colorable. As , it already contains a cycle .
the question says "The graph contain a cycle "
it didnot mention any odd or even length cycle .
so if we take even length then it wiil be 2 .
K5 has nany cycles here he said a cycle ie 1 cycle..
And we have to give minimum color in worst case.. Even will be the best case
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This might help..