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Turán Number of an Induced Complete Bipartite Graph Plus an Odd Cycle

Part of: Graph theory

Published online by Cambridge University Press:  16 July 2018

BEKA ERGEMLIDZE ,
ERVIN GYŐRI  and
ABHISHEK METHUKU
BEKA ERGEMLIDZE
Affiliation:
Department of Mathematics, Central European University, 1051 Budapest, Nádor utca 9 (e-mail: beka.ergemlidze@gmail.com, abhishekmethuku@gmail.com)
ERVIN GYŐRI
Affiliation:
MTA Rényi Institute, 1053 Budapest, Reáltanoda utca 13-15 and Department of Mathematics, Central European University, 1051 Budapest, Nádor utca 9 (e-mail: gyori.ervin@renyi.mta.hu)
ABHISHEK METHUKU
Affiliation:
Department of Mathematics, Central European University, 1051 Budapest, Nádor utca 9 (e-mail: beka.ergemlidze@gmail.com, abhishekmethuku@gmail.com)
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Abstract

Let k ⩾ 2 be an integer. We show that if s = 2 and t ⩾ 2, or s = t = 3, then the maximum possible number of edges in a C2k+1-free graph containing no induced copy of Ks,t is asymptotically equal to (t − s + 1)1/s(n/2)2−1/s except when k = s = t = 2.

This strengthens a result of Allen, Keevash, Sudakov and Verstraëte [1], and answers a question of Loh, Tait, Timmons and Zhou [14].

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05C69: Dominating sets, independent sets, cliques
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 2 , March 2019 , pp. 241 - 252
Copyright
Copyright © Cambridge University Press 2018 

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References

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