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Maximum Δ-edge-colorable subgraphs of class II graphs

✍ Scribed by Vahan V. Mkrtchyan; Eckhard Steffen

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
180 KB
Volume
70
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

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

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