Spectral Perspectives on FAT Graph Colorings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910160502390784 |
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| author | Beers, Lies Mulas, Raffaella |
| author_facet | Beers, Lies Mulas, Raffaella |
| contents | We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while the remaining neighbors are required to be distributed evenly among the other coloring classes. In particular, we determine the FAT chromatic number for all complete multipartite graphs, and we analyze the behavior of FAT colorings under several graph operations. Although spectral methods form the primary focus, several combinatorial arguments are included to complement the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Perspectives on FAT Graph Colorings Beers, Lies Mulas, Raffaella Combinatorics Spectral Theory We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while the remaining neighbors are required to be distributed evenly among the other coloring classes. In particular, we determine the FAT chromatic number for all complete multipartite graphs, and we analyze the behavior of FAT colorings under several graph operations. Although spectral methods form the primary focus, several combinatorial arguments are included to complement the results. |
| title | Spectral Perspectives on FAT Graph Colorings |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2604.21665 |