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arXiv · 1201.4472

A remark on Petersen coloring conjecture of Jaeger

Vahan V. Mkrtchyan
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Abstract

If $G$ and $H$ are two cubic graphs, then we write $H\prec G$, if $G$ admits a proper edge-coloring $f$ with edges of $H$, such that for each vertex $x$ of $G$, there is a vertex $y$ of $H$ with $f(\partial_G(x))=\partial_H(y)$. Let $P$ and $S$ be the Petersen graph and the Sylvester graph, respectively. In this paper, we introduce the Sylvester coloring conjecture. Moreover, we show that if $G$ is a connected bridgeless cubic graph with $G\prec P$, then $G=P$. Finally, if $G$ is a connected cubic graph with $G\prec S$, then $G=S$.

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Vahan V. Mkrtchyan. 2012-07-24. A remark on Petersen coloring conjecture of Jaeger. https://arxiv.org/abs/1201.4472

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