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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00574 |
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| _version_ | 1866909424232169472 |
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| author | Aguilar, Bruno Barik, Daibik Bhambhu, Jetharam Frankel, Evan Nguyen, Nam Hung Tran Mandava, Revathi Marco, Aiden Pon, Kyle Shende, Tejas Wang, Yi |
| author_facet | Aguilar, Bruno Barik, Daibik Bhambhu, Jetharam Frankel, Evan Nguyen, Nam Hung Tran Mandava, Revathi Marco, Aiden Pon, Kyle Shende, Tejas Wang, Yi |
| contents | The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are disjoint unions of graphs. We will derive a general relationship between the asymmetric coloring number of disjoint copies of graphs and the number of ways to color a single copy asymmetrically, and then look at particular cases such as disjoint copies of paths, stars, cycles, and hypercubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymmetric Colorings of Disjoint Unions of Graphs Aguilar, Bruno Barik, Daibik Bhambhu, Jetharam Frankel, Evan Nguyen, Nam Hung Tran Mandava, Revathi Marco, Aiden Pon, Kyle Shende, Tejas Wang, Yi Combinatorics The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are disjoint unions of graphs. We will derive a general relationship between the asymmetric coloring number of disjoint copies of graphs and the number of ways to color a single copy asymmetrically, and then look at particular cases such as disjoint copies of paths, stars, cycles, and hypercubes. |
| title | Asymmetric Colorings of Disjoint Unions of Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.00574 |