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arXiv · 2302.11035

Color-avoiding connected spanning subgraphs with minimum number of edges

József Pintér·Kitti Varga
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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.

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József Pintér, Kitti Varga. 2024-01-26. Color-avoiding connected spanning subgraphs with minimum number of edges. https://arxiv.org/abs/2302.11035

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