Maximum Δ‐edge‐colorable subgraphs of class II graphs |
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| Authors: | Vahan V Mkrtchyan Eckhard Steffen |
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| Institution: | Paderborn Institute for Advanced Studies in Computer Science and Engineering Paderborn University, , Paderborn, Warburger str. 100 33098, Germany |
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| 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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| Keywords: | maximum Δ ‐edge‐colorable subgraph matching 2‐factor edge‐chromatic number chromatic index class II graph |
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