The maximum 2-edge-colorable subgraph problem and its fixed-parameter tractability - Mkrtchyan, Vahan (Journal of Graph Algorithms and Applications, 2024)
A k-edge-coloring of a graph is an assignment of colors {1,...,k} to edges of the graph such that adjacent edges receive different colors. In the maximum k-edge-colorable subgraph problem we are given a graph and an integer k, the goal is to find a k-edge-colorable subgraph with maximum number of edges together with its k-edge-coloring. In this paper, we consider the maximum 2-edge-colorable subgraph problem and present some results that deal with the fixed-parameter tractability of this problem.