On disjoint matchings in cubic graphs

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

No reviews yet.

No comments yet.