On disjoint matchings in cubic graphs: Maximum 2-edge-colorable and maximum 3-edge-colorable subgraphs.

Abstract: We show that any 2-factor of a cubic graph can be extended to a maximum 3-edge-colorable subgraph. We also show that the sum of sizes of maximum 2- and 3-edge-colorable subgraphs of a cubic graph is at least twice of its number of vertices. Finally, for a cubic graph , consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let be the largest matching among such pairs. Let be a maximum matching of . We show that is a tight upper bound for . [Copyright &y& Elsevier]