On disjoint matchings in cubic graphs

Abstract

For $i=2,3$ and a cubic graph $G$ let ${\nu }_i(G)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that ${\nu }_2(G)\ge 4/5|V(G)|$ and ${\nu }_3(G)\ge 7/6|V(G)|$. Moreover, it turns out that ${\nu }_2(G)\le \frac{|V(G)|+2{\nu }_3(G)}{4}$.

41 pages, 8 figures, minor chages

References in corpus (4)

• 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)

• On disjoint matchings in cubic graphs: maximum 2- and 3-edge-colorable subgraphs
• Maximum $\Delta$-edge-colorable subgraphs of class II graphs
• 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