, Volume 29, Issue 5, pp 1305-1309,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 08 Aug 2012

A Note on Turán Numbers for Even Wheels


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, W 2k ) 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.