A bound on the number of edges in graphs without an even cycle

Abstract

We show that, for each fixed $k$, an $n$-vertex graph not containing a cycle of length $2k$ has at most $80\sqrt{k}\log k\cdot n^{1+1/k}+O(n)$ edges.

16 pages, v2 appeared in Comb. Probab. Comp., v3 fixes an error in v2 and explains why the method in the paper cannot improve the power of k further, v4 fixes the proof of Theorem 12 introduced in v3

References in corpus (1)

• Turán numbers for $K_{s,t}$-free graphs: topological obstructions and algebraic constructions

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