Fixed-point-free embeddings of digraphs with small size

Görlich, Agnieszka; Pilniak, Monika; Woniak, Mariusz; Zioło, Irmina A.

doi:10.1016/j.disc.2005.11.070

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Cited by 3 publications

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“…The basic ingredient for the proof of our theorem is the lemma presented below. This lemma is both a modification and an extension of Lemma 2 in [4].…”

Section: Introductionmentioning

confidence: 90%

A Note on Packing Graphs Without Cycles of Length up to Five

Görlich¹,

Żak²

2009

Electron. J. Combin.

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The following statement was conjectured by Faudree, Rousseau, Schelp and Schuster: if a graph $G$ is a non-star graph without cycles of length $m \leq 4$ then $G$ is a subgraph of its complement. So far the best result concerning this conjecture is that every non-star graph $G$ without cycles of length $m \leq 6$ is a subgraph of its complement. In this note we show that $m\leq 6$ can be replaced by $m \leq 5$.

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“…The basic ingredient for the proof of our theorem is the lemma presented below. This lemma is both a modification and an extension of Lemma 2 in [4].…”

Section: Introductionmentioning

confidence: 90%