论文标题
嵌入式第II部分的远处2色组件：短期不可分割的情况
Distant 2-Colored Components on Embeddings Part II: The Short-Inseparable Case
论文作者
论文摘要
这是三篇论文序列中的第二个，我们证明了Thomassen的5-毫无用处定理的以下概括：让$ g $是嵌入在$ g $属表面上的图。然后$ g $可以是$ l $颜色的，其中$ l $是$ g $的列表分配，其中每个顶点都有5个列表，除了一系列成对的远距离组件集合，每个顶点都有普通的2彩色的精确度，只要$ g $的面部宽度至少是至少$ 2^{g）$ 2^{ω$ 2^{Ω $ 2^{ω（g）} $。这为Thomassen的猜想的广义版本提供了肯定的答案，并概括了2017年DvoDimák，Lidický，Mohar和Tostle of Tostaint the Extant Pregant的顶点。在本文中，我们证明了上述结果适用于限制类别的嵌入类别，即满足某些三角剖分条件并且最多没有长度周期的嵌入。
This is the second in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is at least $2^{Ω(g)}$ and the precolored components are of distance at least $2^{Ω(g)}$ apart. This provides an affirmative answer to a generalized version of a conjecture of Thomassen and also generalizes a result from 2017 of Dvořák, Lidický, Mohar, and Postle about distant precolored vertices. In this paper we prove that the above result holds for a restricted class of embeddings, i.e. those embeddings which satisfy certain triangulation conditions and do not have separating cycles of length at most four.
