Approximating maximum properly colored forests via degree bounded independent sets
Abstract
In the Maximum-size Properly Colored Forest problem, we are given an edge-colored undirected graph and the goal is to find a properly colored forest with as many edges as possible. We study this problem within a broader framework by introducing the Maximum-size Degree Bounded Matroid Independent Set problem: given a matroid, a hypergraph on its ground set with maximum degree , and an upper bound for each hyperedge , the task is to find a maximum-size independent set that contains at most elements from each hyperedge . We present approximation algorithms for this problem whose guarantees depend only on . When applied to the Maximum-size Properly Colored Forest problem, this yields a -approximation on multigraphs, improving the factor of Bai, B\'erczi, Cs\'aji, and Schwarcz [Eur. J. Comb. 132 (2026) 104269].
Keywords
Cite
@article{arxiv.2511.18263,
title = {Approximating maximum properly colored forests via degree bounded independent sets},
author = {Yuhang Bai and Kristóf Bérczi and Johanna K. Siemelink},
journal= {arXiv preprint arXiv:2511.18263},
year = {2025}
}