arXiv subjects

Samvel S. Petrosyan

Publications and source records attributed to Samvel S. Petrosyan.

3 recordsLinked to original sources

arXiv2012

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

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 $|M|/|H|$.

cs.DM↗

arXiv2010

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 $ν_{2}(G)\leq \frac{|V(G)|+2ν_{3}(G)}{4}$.

cs.DM↗

arXiv2008

5-cycles and the Petersen graph

We show that if G is a connected bridgeless cubic graph whose every 2-factor is comprised of cycles of length five then G is the Petersen graph.

cs.DM↗