首页 / 资料库 / 文献详情

1-平面图的结构性质及其在无圈边染色上的应用

Xin Zhang、建良 吴、Jianliang Wu

2010Scientia Sinica MathematicaComputer Science被引 9开放获取

摘要

A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small vertices (i.e. vertices of degree no more than seven). Meanwhile, some new classes of light graphs in 1-planar graphs with the bounded degree are found. Therefore, two open problems presented by Fabrici and Madaras [The structure of 1-planar graphs, Discrete Mathematics, 307, (2007), 854-865] are solved. Furthermore, we prove that each 1-planar graph $G$ with maximum degree $\Delta(G)$ is acyclically edge $L$-choosable where $L=\max\{2\Delta(G)-2,\Delta(G)+83\}$.

引用本文（GB/T 7714）

DOI：https://doi.org/10.1360/012009-678