论文标题
嵌入式第I部分：连接面的遥远的2色组件
Distant 2-Colored Components on Embeddings Part I: Connecting Faces
论文作者
论文摘要
这是三篇论文序列中的第一篇，我们证明了托马森（Thomassen）的5-毫无用处定理的以下概括：让$ g $是嵌入在$ g $属表面上的有限图。 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 $2^{Ω(g)}$ and the precolored components are of distance $2^{Ω(g)}$除外。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。
This is the first in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite 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 $2^{Ω(g)}$ and the precolored components are of distance $2^{Ω(g)}$ 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.
