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arXiv · 2409.15388

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

Vahan Mkrtchyan
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Abstract

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 of $G$ such that their union contains maximum number of edges. This problem is NP-hard in cubic graphs, and polynomial-time solvable in bipartite graphs as we observe in our paper. We present an NP-hardness result for a version of this problem where we have color constraints on vertices. In fact, we show that this version is NP-hard already in bipartite graphs of maximum degree three. In order to achieve the result, we establish a connection between our problem and the problem of construction of special maximum matchings considered in the Master thesis of the author and defended back in 2003.

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Vahan Mkrtchyan. 2024-09-22. An NP-hardness result for the colored constrained maximum 2-edge-colorable subgraph problem in bipartite graphs. https://arxiv.org/abs/2409.15388

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