ON STRONGLY SPANNING k-EDGE-COLORABLE SUBGRAPHS.

A subgraph H of a multigraph G is called strongly spanning, if any vertex of G is not isolated in H. H is called maximum k-edge-colorable, if H is proper k-edge-colorable and has the largest size. We introduce a graph-parameter sp(G), that coincides with the smallest k for which a multigraph G has a maximum k-edge-colorable subgraph that is strongly spanning. Our first result offers some alternative definitions of sp(G). Next, we show that △(G) is an upper bound for sp(G), and then we characterize the class of multigraphs G that satisfy sp(G) = △(G). Finally, we prove some bounds for sp(G) that involve well-known graph-theoretic parameters. [ABSTRACT FROM AUTHOR]