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arXiv · 0909.2767

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

Davit Aslanyan·Vahan V. Mkrtchyan·Samvel S. Petrosyan·Gagik N. Vardanyan
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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 $|M|/|H|$.

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Davit Aslanyan, Vahan V. Mkrtchyan, Samvel S. Petrosyan, Gagik N. Vardanyan. 2009-09-15. On disjoint matchings in cubic graphs: maximum 2- and 3-edge-colorable subgraphs. https://doi.org/10.1016/j.dam.2014.03.001

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