Corpus ID: 15177037

Graphs, Disjoint Matchings and Some Inequalities

@article{Hambardzumyan2015GraphsDM,
  title={Graphs, Disjoint Matchings and Some Inequalities},
  author={Lianna Hambardzumyan and V. Mkrtchyan},
  journal={arXiv: Discrete Mathematics},
  year={2015}
}
For $k \geq 1$ and a graph $G$ let $\nu_k(G)$ denote the size of a maximum $k$-edge-colorable subgraph of $G$. Mkrtchyan, Petrosyan and Vardanyan proved that $\nu_2(G)\geq \frac45\cdot |V(G)|$, $\nu_3(G)\geq \frac76\cdot |V(G)|$ for any cubic graph $G$ ~\cite{samvel:2010}. They were also able to show that if $G$ is a cubic graph, then $\nu_2(G)+\nu_3(G)\geq 2\cdot |V(G)|$ ~\cite{samvel:2014} and $\nu_2(G) \leq \frac{|V(G)| + 2\cdot \nu_3(G)}{4}$ ~\cite{samvel:2010}. In the first part of the… Expand
On maximum k-edge-colorable subgraphs of bipartite graphs
TLDR
The result implies that if the cubic graph G contains a perfect matching, in particular when it is bridgeless, then ν 2 ( G) ≤ ν 1 ( G ) + ν 3 ( G ), which is the number of edges of a maximum k -edge-colorable subgraph of G. Expand

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