关于Jaeger的Petersen着色猜想的注记
A remark on Petersen coloring conjecture of Jaeger
摘要：
如果$G$和$H$是两个三次图，则我们记为$H\prec G$，如果$G$允许一个具有$H$的边的适当边染色$f$，使得对于$G$的每个顶点$x$，都有一个具有$f(\partial_G(x))=\partial_H(y)$的$H$的顶点$y$.设$P$和$S$分别是Petersen图和Sylvester图。本文介绍了Sylvester着色猜想。此外，我们还证明了如果$G$是一个连通无桥三次图，且有$G\prec P$，则有$G=P$ .最后，如果$G$是一个连通三次图，且有$G\prec S$，则有$G=S$ .
英文摘要：
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 $G=S$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
