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(G)∣∣E(H)∣, 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.Comment: 13 pages, 2 figures, the proof of the Lemma 1 is correcte