Maximum Δ‐edge‐colorable subgraphs of class II graphs
Maximum Δ‐edge‐colorable subgraphs of class II graphs
复制标题
II 类图的最大 Δ 边可着色子图
DOI：
10.1002/jgt.20629
复制
发表时间：
2010
影响因子：
0.9
通讯作者：
E. Steffen
中科院分区：
文献类型：
--
作者：
V. Mkrtchyan;E. Steffen
图G是II类，如果它的色指数至少为Δ + 1。设H为G的极大Δ‐‐可着色子图，证明了|E(H)|/|E(G)|的最佳可能下界，以及极大Δ‐‐可着色子图的结构性质。证明了具有Δ≥3的第II类图的每个顶点不相交环集都可以推广到一个极大的Δ‐边‐可着色子图。简单图有一个极大的Δ‐边‐可着色子图，使得补是匹配的。此外，简单图的最大Δ‐边‐可着色子图总是类i©2011 Wiley Periodicals， Inc.。J图论
A graph G is class II, if its chromatic index is at least Δ + 1. Let H be a maximum Δ‐edge‐colorable subgraph of G. The paper proves best possible lower bounds for |E(H)|/|E(G)|, and structural properties of maximum Δ‐edge‐colorable subgraphs. It is shown that every set of vertex‐disjoint cycles of a class II graph with Δ≥3 can be extended to a maximum Δ‐edge‐colorable subgraph. Simple graphs have a maximum Δ‐edge‐colorable subgraph such that the complement is a matching. Furthermore, a maximum Δ‐edge‐colorable subgraph of a simple graph is always class I. © 2011 Wiley Periodicals, Inc. J Graph Theory