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A Bound on the Number of Edges in Graphs Without an Even Cycle

Published online by Cambridge University Press:  07 April 2016

BORIS BUKH
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: bbukh@math.cmu.edu)
ZILIN JIANG
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: zj@cmu.edu)

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.

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Copyright
Copyright © Cambridge University Press 2016 

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