Graphs and Combinatorics

, Volume 29, Issue 5, pp 1305–1309 | Cite as

A Note on Turán Numbers for Even Wheels

Open Access
Original Paper

Abstract

The Turán number ex(n, G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. We consider a very special case of the Simonovits’s theorem (Simonovits in: Theory of graphs, Academic Press, New York, 1968) which determine an asymptotic result for Turán numbers for graphs with some properties. In the paper we present a more precise result for even wheels. We provide the exact value for Turán number ex(n, W2k) for n ≥ 6k − 10 and k ≥ 3. In addition, we show that \({ex(n,W_6)= \lfloor\frac{n^2}{3}\rfloor}\) for all n ≥ 6. These numbers can be useful to calculate some Ramsey numbers.

Keywords

Turán problem Cycles 

Mathematics Subject Classification (2000)

05C35 05C38 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of GdańskGdańskPoland

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