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

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  07 April 2016

BORIS BUKH  and
ZILIN JIANG
BORIS BUKH
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: [email protected])
ZILIN JIANG
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: [email protected])
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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.

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05D99: None of the above, but in this section 05C38: Paths and cycles
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 1 , January 2017 , pp. 1 - 15
Copyright
Copyright © Cambridge University Press 2016 

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