Graphs and Combinatorics

, Volume 29, Issue 5, pp 1305–1309

A Note on Turán Numbers for Even Wheels

Open AccessOriginal Paper

DOI: 10.1007/s00373-012-1212-9

Cite this article as:
Dzido, T. Graphs and Combinatorics (2013) 29: 1305. doi:10.1007/s00373-012-1212-9

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 problemCycles

Mathematics Subject Classification (2000)

05C3505C38
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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of GdańskGdańskPoland