On the structure of linear graphs
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- Erdös, P. Israel J. Math. (1963) 1: 156. doi:10.1007/BF02759702
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Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n2/4]+1) contains a circuit ofl edges for every 3 ≦l<c2n, also that everyG(n; [n2/4]+1) contains ake(un, un) withun=[c1 logn] (for the definition ofke(un, un) see the introduction). Finally fort>t0 everyG(n; [tn3/2]) contains a circuit of 2l edges for 2≦l<c3t2.