Fair and Tolerant (FAT) Graph Colorings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914155643011072 |
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| author | Beers, Lies Mulas, Raffaella |
| author_facet | Beers, Lies Mulas, Raffaella |
| contents | We introduce and study Fair and Tolerant colorings (FAT colorings), where each vertex tolerates a given fraction of same-colored neighbors while fairness is preserved across the other coloring classes. Moreover, we define the FAT chromatic number $χ^{\mathrm{FAT}}(G)$ as the largest integer $k$ for which $G$ admits a FAT $k$-coloring. We establish general bounds on $χ^{\mathrm{FAT}}$, relate it to structural and spectral properties of graphs, and characterize it completely for several families of graphs. We conclude with a list of open questions that suggest future directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fair and Tolerant (FAT) Graph Colorings Beers, Lies Mulas, Raffaella Combinatorics Spectral Theory We introduce and study Fair and Tolerant colorings (FAT colorings), where each vertex tolerates a given fraction of same-colored neighbors while fairness is preserved across the other coloring classes. Moreover, we define the FAT chromatic number $χ^{\mathrm{FAT}}(G)$ as the largest integer $k$ for which $G$ admits a FAT $k$-coloring. We establish general bounds on $χ^{\mathrm{FAT}}$, relate it to structural and spectral properties of graphs, and characterize it completely for several families of graphs. We conclude with a list of open questions that suggest future directions. |
| title | Fair and Tolerant (FAT) Graph Colorings |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2510.18494 |