On disjoint matchings in cubic graphs: maximum 2- and 3-edge-colorable subgraphs
| Autor: | Aslanyan, Davit, Mkrtchyan, Vahan V., Petrosyan, Samvel S., Vardanyan, Gagik N. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Discrete Applied Mathematics 172 (2014) pp. 12--27 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.dam.2014.03.001 |
| Popis: | 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 $|M|/|H|$. Comment: 31 pages, 14 figures, majorly revised |
| Databáze: | arXiv |
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