[Graphs]IIT-k Written test

Question

Graph Matching was explained. Let $S$ and $R$ be the matching graph, then a new graph $G=(S-R) \cup (R-S)$, will be union of vertex disjoint path and cycle. Also prove that the cycle obtained will be of even length.

Comments

@Rahul ,Could you please explain , what  is matching graph ? and in IITs' interview , should we have to give formal proof or is it ok if we prove it by counterexamples ?

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I am not sure. I found this question in interview experience

I copy pasted as it is. :(

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@rahul sharma 5 could you provide the link to question where you have found ??