A note on embedding graphs without short cycles Original Research Article

Let k⩾3 be an integer. Denote by Tk the following statement: If a graph G is a non-star graph without cycles of length ⩽k then G is a subgraph of its complement. It has been conjectured by Faudree, Rousseau, Schelp and Schuster that T4 holds. As far as we know the best general result is in the paper of Brandt who proved that T6 holds. In this paper we give an another, relatively short proof of Brandtʹs result.