Elsevier

Discrete Mathematics

Volume 286, Issues 1–2, 6 September 2004, Pages 75-77
Discrete Mathematics

A note on embedding graphs without short cycles

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Abstract

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 Brandt's result.

Keywords

Embedding of graphs
Cycles
Embedding without fixed points

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