Four-cycles in graphs without a given even cycle

Authors:
Daniela Kühn;Deryk Osthus
Affiliations:
Freie Universität Berlin, Institut für Mathematik, Arnimallee 2–6, D-14195 Berlin, Germany;Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
Venue:
Journal of Graph Theory
Year:
2005

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Approximating Maximum Subgraphs without Short Cycles

APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximating Maximum Subgraphs without Short Cycles

SIAM Journal on Discrete Mathematics

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Abstract

We prove that every bipartite C2l-freegraph G contains a C4-free subgraphH with e(H) ≥ e(G)-(l1). The factor 1-(l 1) is best possible. This implies thatex(n, C2l) ≤ 2(l1)ex(n, {C4,C2l}), which settles a special case of aconjecture of Erdõs and Simonovits. © 2004 WileyPeriodicals, Inc. J Graph Theory 48: 147156, 2005