论文标题
Thomassen定理的扩展至最多四个：第二部分
Extensions of Thomassen's Theorem to Paths of Length At Most Four: Part II
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 $至少列出了三个大小的列表。这是第二篇论文的第二篇论文，我们证明了有关部分$ l $ colorings $ c $的$ c $ $ c $的一些结果，该属性的任何扩展为$ l $ - 颜色的$ \ textrm {dom} {dom}（ϕ）\ cup v（p）$ to $ l $ l $ - $ color your-color your-color your-color your-c $ g $ your-c $ g $ y your-g $ y of your-c $ g $ g $ g $ $ \ textrm {dom}（ϕ）$仅由$ p $的端点组成。我们还证明了有关其他特殊情况的一些结果，其中$ c \ setMinus \ Mathring {p} $允许$ ϕ $上色，但我们避免将太多颜色从$ \ Mathring {p} \ setMinus \ setMinus \ textrm {dom}（ϕ）$中取出。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. This is the second paper in a sequence of three papers in which 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 $G$, and, in particular, some useful results about the special case in which $\textrm{dom}(ϕ)$ consists only of the endpoints of $P$. We also prove some results about the other special case in which $ϕ$ is allowed to color some vertices of $C\setminus\mathring{P}$ but we avoid taking too many colors away from the leftover vertices of $\mathring{P}\setminus\textrm{dom}(ϕ)$. We use these results in a later sequence of papers to prove some results about list-colorings of high-representativity embeddings on surfaces.
