Maximum ?-edge-colorable subgraphs of class II graphs
A graph G is class II, if its chromatic index is at least ? + 1. Let H be a maximum ?-edge-colorable subgraph of G. The paper proves best possible lower bounds for |E(H)|/|E(G)|, and structural properties of maximum ?-edge-colorable subgraphs. It is shown that every set of vertex-disjoint cycles of a class II graph with ??3 can be extended to a maximum ?-edge-colorable subgraph. Simple graphs have a maximum ?-edge-colorable subgraph such that the complement is a matching. Furthermore, a maximum ?-edge-colorable subgraph of a simple graph is always class I.  2011 Wiley Periodicals, Inc. J Graph Theory
maximum ?-edge-colorable subgraph class ii graph chromatic index matching 2-factor edge-chromatic number