论文标题
Thomassen定理的一些扩展到更长的路径
Some Extensions of Thomassen's Theorem to Longer Paths
论文作者
论文摘要
让$ g $是带有列表分配$ l $和外部周期$ c $的平面嵌入，让$ p $是$ c $上最多的四个途径，在$ c $上，每个顶点$ g \ setminus c $ c $ c $ co $ co $ co $ co $的大小至少列出了五个，每个顶点$ c \ c \ setminus p $至少列出了三个大小的列表。在本文中，我们证明了有关部分$ l $颜色的$ c $ $ c $的一些结果，该属性将$ ϕ $的任何扩展到$ l $ - 颜色的$ \ textrm {dom} {dom}（ϕ）\ cup v（p）$扩展到$ l $ l $ - $ l $ color-color-color-color- $ g $的全部$ g $。我们将这些结果在以后的论文序列中使用，以证明有关表面上高呈现性嵌入的列表色的一些结果。
Let $G$ be a planar embedding with list-assignment $L$ and outer cycle $C$, and let $P$ be a path of length at most four on $C$, where each vertex of $G\setminus C$ has a list of size at least five and each vertex of $C\setminus P$ has a list of size at least three. In this paper, we prove some results about partial $L$-colorings $ϕ$ of $C$ with the property that any extension of $ϕ$ to an $L$-coloring of $\textrm{dom}(ϕ)\cup V(P)$ extends to $L$-color all of $G$. We use these results in a later sequence of papers to prove some results about list-colorings of high-representativity embeddings on surfaces.
