Prove that if $$ is a graph that $| () | ≥ | () | +4$ then $$ contains at least two disjoint edge cycles.
I have no idea about this question! Please help me to prove it.
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1What is an edge round? – Alma Arjuna Oct 19 '20 at 17:51
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@Arjuna196 round is enough and I should delete the edge! – user808266 Oct 19 '20 at 18:02
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What do you mean by edge round? Can you give a definition? It is very unclear. – Mathieu Rundström Oct 19 '20 at 18:09
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1From the context, it looks like 'separate rounds' means disjoint edge cycles. – Alvin Jin Oct 19 '20 at 18:22
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Hint: you can do casework and reduce this to the case when all vertices have degree 3 or more. – Alvin Jin Oct 19 '20 at 18:24
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You're right.My English is weak and this has become a big problem!Now I corrected the question.Is this OK?@MishaLavrov – user808266 Oct 19 '20 at 19:54
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Yes, this is better. – Misha Lavrov Oct 19 '20 at 21:01
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What is an "edge cycle"? Do you mean "edge-disjoint cycles", i.e., two cycles having no edge in common, although they may have vertices in common? – bof Oct 19 '20 at 23:37