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- Vahan V. Mkrtchyan, Samvel S. Petrosyan, Gagik N. Vardanyan
- Discrete Mathematics
- 2010

In this paper graphs are assumed to be finite, undirected and without loops, though they may contain multiple edges. We will also consider pseudo-graphs, which, in contrast with graphs, may containâ€¦ (More)

For k â‰¥ 1 and a graphG let Î½k(G) denote the size of a maximum k-edge-colorable subgraph of G. Mkrtchyan, Petrosyan and Vardanyan proved that Î½2(G) â‰¥ 4 5 Â· |V (G)|, Î½3(G) â‰¥ 7 6 Â· |V (G)| for any cubicâ€¦ (More)

- Vahan V. Mkrtchyan, Eckhard Steffen
- Discrete Mathematics
- 2012

The resistance r(G) of a graph G is the minimum number of edges that have to be removed from G to obtain a graph which is âˆ†(G)-edge-colorable. The paper relates the resistance to other parametersâ€¦ (More)

- Raffi R. Kamalian, Vahan V. Mkrtchyan
- ArXiv
- 2007

For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by itsâ€¦ (More)

- Vahan V. Mkrtchyan
- Discrete Mathematics
- 2006

I prove that in a tree in which the distance between any two endpoints is even, there is a maximum proper partial 0 âˆ’ 1 coloring such that the edges colored by 0 form a maximum matching.

- Vahan V. Mkrtchyan
- Discrete Mathematics
- 2006

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.

- Vahan V. Mkrtchyan, Eckhard Steffen
- Journal of Graph Theory
- 2012

A graph G is class II, if its chromatic index is at least âˆ† + 1. Let H be a maximum âˆ†-edge-colorable subgraph of G. The paper proves best possible lower bounds for |E(H)| |E(G)| , and structuralâ€¦ (More)

- Davit Aslanyan, Vahan V. Mkrtchyan, Samvel S. Petrosyan, Gagik N. Vardanyan
- Discrete Applied Mathematics
- 2014

We show that any 2âˆ’factor of a cubic graph can be extended to a maximum 3âˆ’edge-colorable subgraph. We also show that the sum of sizes of maximum 2âˆ’ and 3âˆ’edge-colorable subgraphs of a cubic graph isâ€¦ (More)

- Vahan V. Mkrtchyan
- Australasian J. Combinatorics
- 2013

If G and H are two cubic graphs, then we write H â‰º G if G admits a proper edge-coloring f with edges of H, such that for each vertex x of G, there is a vertex y of H with f(âˆ‚G(x)) = âˆ‚H(y). Let P andâ€¦ (More)

- Vahan V. Mkrtchyan, Vahe L. Musoyan, A. V. Tserunyan
- Discrete Mathematics
- 2008

For a 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. Weâ€¦ (More)