Color-avoiding connected spanning subgraphs with minimum number of edges
Abstract
We call a (not necessarily properly) edge-colored graph edge-color-avoiding connected if after the removal of edges of any single color, the graph remains connected. For vertex-colored graphs, similar definitions of color-avoiding connectivity can be given. In this article, we investigate the problem of determining the maximum number of edges that can be removed from a color-avoiding connected graph so that it remains color-avoiding connected. First, we prove that this problem is NP-hard, then we give a polynomial-time approximation algorithm for it. To analyze the approximation factor of this algorithm, we determine the minimum number of edges of color-avoiding connected graphs on a given number of vertices and with a given number of colors. Furthermore, we also consider a generalization of edge-color-avoiding connectivity to matroids.
Cite
@article{arxiv.2302.11035,
title = {Color-avoiding connected spanning subgraphs with minimum number of edges},
author = {József Pintér and Kitti Varga},
journal= {arXiv preprint arXiv:2302.11035},
year = {2024}
}