In a simple graph G, what is the maximum bound for edges if we want shortest cycle stay at k.
How we can find this bound for a graph? Have it any formula or technique to calculate it?
thanks in advance
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Assuming $k$ divides $n$, you could construct a ring of size $n$ and then insert hoops of lengths up to $n/k$. I don't know if it is tight, but it does feel like a worst case. – dtldarek Nov 02 '16 at 09:28
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Case $k=4$ – Alex Ravsky Nov 07 '16 at 08:19
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Look also parts of this thread related to girth. – Alex Ravsky Nov 07 '16 at 09:21