Infinite graphs that do not contain cycles of length four
classification
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math.NT
keywords
containcyclesfourgraphsinfinitelengthconstructcountable
read the original abstract
We construct a countable infinite graph G that does not contain cycles of length four having the property that the sequence of graphs $G_n$ induced by the first $n$ vertices has minimum degree $\delta(G_n)> n^{\sqrt{2}-1+o(1)}$.
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