On disjoint matchings in cubic graphs: maximum 2- and 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 $G$, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let $H$ be the largest matching among such pairs. Let $M$ be a maximum matching of $G$. We show that 9/8 is a tight upper bound for $|M|/|H|$.

31 pages, 14 figures, majorly revised

References in corpus (5)

• On disjoint matchings in cubic graphs
• On trees with a maximum proper partial 0-1 coloring containing a maximum matching
• A note on minimal matching covered graphs
• On Edge-Disjoint Pairs Of Matchings
• Characterization Of A Class Of Graphs Related To Pairs Of Disjoint Matchings

Cited by in corpus (5)

• Maximum $\Delta$-edge-colorable subgraphs of class II graphs
• Maximal $k$-Edge-Colorable Subgraphs, Vizing's Theorem, and Tuza's Conjecture
• Assigning tasks to agents under time conflicts: a parameterized complexity approach
• Pairs of disjoint matchings and related classes of graphs
• Graphs, Disjoint Matchings and Some Inequalities