Color-avoiding connected colorings and orientations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908521363144704 |
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| author | Pintér, József Varga, Kitti |
| author_facet | Pintér, József Varga, Kitti |
| contents | We study network robustness under correlated failures modeled by colors, where each color represents a class of edges or vertices that may fail simultaneously. An edge-colored graph is said to be edge-color-avoiding $k$-edge-connected if it remains $k$-edge-connected after the removal of all edges of any single color. We characterize the graphs that admit such a coloring and show that, when $k = 1$, one can determine in polynomial time both the minimum number of colors required and a coloring achieving it; while the problem becomes NP-hard for $k \ge 2$. We also investigate the problem of orienting the edges of a graph so that the resulting digraph remains strongly or rooted connected even after the removal of all arcs of any single color. In addition, we explore generalizations involving vertex-colorings, $k$-vertex-connectivity, simultaneous failures of multiple colors and matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Color-avoiding connected colorings and orientations Pintér, József Varga, Kitti Combinatorics We study network robustness under correlated failures modeled by colors, where each color represents a class of edges or vertices that may fail simultaneously. An edge-colored graph is said to be edge-color-avoiding $k$-edge-connected if it remains $k$-edge-connected after the removal of all edges of any single color. We characterize the graphs that admit such a coloring and show that, when $k = 1$, one can determine in polynomial time both the minimum number of colors required and a coloring achieving it; while the problem becomes NP-hard for $k \ge 2$. We also investigate the problem of orienting the edges of a graph so that the resulting digraph remains strongly or rooted connected even after the removal of all arcs of any single color. In addition, we explore generalizations involving vertex-colorings, $k$-vertex-connectivity, simultaneous failures of multiple colors and matroids. |
| title | Color-avoiding connected colorings and orientations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.05143 |