单环平面图的奇面全着色

IF 1 Q1 MATHEMATICS
J. Czap
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引用次数: 0

摘要

平面图G的面全着色是顶点和边缘的着色,使得没有面相邻的边(在G的面边界行走上连续的边),没有相邻的顶点,没有边缘及其顶点被赋予相同的颜色。如果对于每个面f和每个颜色c,没有元素或与f相关的元素的奇数个元素被c着色,则G的面总着色为奇数。证明了每一个单环平面图都存在一个最多10种颜色的奇面全着色。还证明了这个界是紧的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Odd Facial Total-Coloring of Unicyclic Plane Graphs
A facial total-coloring of a plane graph G is a coloring of the vertices and edges such that no facially adjacent edges (edges that are consecutive on the boundary walk of a face of G ), no adjacent vertices, and no edge and its endvertices are assigned the same color. A facial total-coloring of G is odd if for every face f and every color c , either no element or an odd number of elements incident with f is colored by c . In this paper, it is proved that every unicyclic plane graph admits an odd facial total-coloring with at most 10 colors. It is also shown that this bound is tight.
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来源期刊
Discrete Mathematics Letters
Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.50
自引率
12.50%
发文量
47
审稿时长
12 weeks
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