V. Mkrtchyan

activity

20072026

most citedOn disjoint matchings in cubic graphs

20 citations · 146 across the 41 of their papers we have counts for

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10 papers · 1 filter

math.CO2026

Some new results on Sylvester colorings of cubic graphs

Luca Ferrarini, Vahan Mkrtchyan

If $G$ and $H$ are two cubic multi-graphs, then an $H$ -coloring of $G$ is a mapping $f : E (G) \to E (H)$ , such that for every $v \in V (G)$ there is a vertex $x \in V (H)$ , such t…

math.CO2025

Expanding vertices to triangles in cubic graphs

Giuseppe Mazzuoccolo, Vahan Mkrtchyan

Contraction of triangles is a standard operation in the study of cubic graphs, as it reduces the order of the graph while typically preserving many of its properties. In this paper…

math.CO2024

Non-conflicting no-where zero $Z_{2} \times Z_{2}$ flows in cubic graphs

Vahan Mkrtchyan

Let $Z_{2} \times Z_{2} = {0, α, β, α + β}$ . If $G$ is a bridgeless cubic graph, $F$ is a perfect matching of $G$ and $F$ is the complementary 2-factor of $F$ , then a no-where…

math.CO2024★ 1 cited

Three results towards the approximation of special maximum matchings in graphs

Vahan Mkrtchyan

For a graph $G$ define the parameters $ℓ (G)$ and $L (G)$ as the minimum and maximum value of $ν (G \ F)$ , where $F$ is a maximum matching of $G$ and $ν (G)$ is the matching…

math.CO2024★ 1 cited

An NP-hardness result for the colored constrained maximum 2-edge-colorable subgraph problem in bipartite graphs

Vahan Mkrtchyan

In this paper, we consider the maximum $k$ -edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$ , the goal is to take $k$ matchings o…

math.CO2024

Block graphs - some general results and their equitable colorings

Hanna Furmańczyk, Vahan Mkrtchyan

In this paper, we consider some general properties of block graphs as well as the equitable coloring problem in this class of graphs. In the first part we establish the relation be…

math.CO2022

Decomposition of class II graphs into two class I graphs

Yan Cao, Guangming Jing, Rong Luo +3

Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum $Δ$ -edge-colorable subgraph and a matching.…

math.CO2020★ 3 cited

Some snarks are worse than others

Edita Máčajová, Giuseppe Mazzuoccolo, Vahan Mkrtchyan +1

Many conjectures and open problems in graph theory can either be reduced to cubic graphs or are directly stated for cubic graphs. Furthermore, it is known that for a lot of problem…

math.CO2015★ 3 cited

On Sylvester Colorings of Cubic Graphs

Anush Hakobyan, Vahan Mkrtchyan

If $G$ and $H$ are two cubic graphs, then an $H$ -coloring of $G$ is a proper edge-coloring $f$ with edges of $H$ , such that for each vertex $x$ of $G$ , there is a vertex $y$ of $H$ …

math.CO2015

Graph Theory

Petros A. Petrosyan, Vahan V. Mkrtchyan, Rafayel R. Kamalian

This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University.

Some new results on Sylvester colorings of cubic graphs

Expanding vertices to triangles in cubic graphs

Non-conflicting no-where zero Z2​×Z2​ flows in cubic graphs

Three results towards the approximation of special maximum matchings in graphs

An NP-hardness result for the colored constrained maximum 2-edge-colorable subgraph problem in bipartite graphs

Block graphs - some general results and their equitable colorings

Decomposition of class II graphs into two class I graphs

Some snarks are worse than others

On Sylvester Colorings of Cubic Graphs

Graph Theory

Non-conflicting no-where zero $Z_{2} \times Z_{2}$ flows in cubic graphs