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Extremal Numbers for Odd Cycles

Published online by Cambridge University Press:  01 December 2014

ZOLTAN FÜREDI  and
DAVID S. GUNDERSON
ZOLTAN FÜREDI
Affiliation:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13–15, H-1053, Budapest, Hungary (e-mail: z-furedi@illinois.edu, furedi.zoltan@renyi.mta.hu)
DAVID S. GUNDERSON
Affiliation:
Department of Mathematics, University of Manitoba, 521 Machray Hall, Winnipeg, Manitoba R3T 2N2, Canada (e-mail: David.Gunderson@umanitoba.ca)
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Abstract

We describe the C2k+1-free graphs on n vertices with maximum number of edges. The extremal graphs are unique for n ∉ {3k − 1, 3k, 4k − 2, 4k − 1}. The value of ex(n, C2k+1) can be read out from the works of Bondy [3], Woodall [14], and Bollobás [1], but here we give a new streamlined proof. The complete determination of the extremal graphs is also new.

We obtain that the bound for n0(C2k+1) is 4k in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turán graph.

Keywords

Primary 05C35Secondary 05D99

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Special Issue 4: Oberwolfach Special Issue Part 1 , July 2015 , pp. 641 - 645
Copyright
Copyright © Cambridge University Press 2014 

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