Some progress on $t$-tone coloring
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914094179680256 |
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| author | Bennett, Patrick Nichols, Jade |
| author_facet | Bennett, Patrick Nichols, Jade |
| contents | A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For example we prove a new result for trees of large maximum degree, as well as some results for the cartesian power of a graph. We also make a conjecture about trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some progress on $t$-tone coloring Bennett, Patrick Nichols, Jade Combinatorics Discrete Mathematics A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For example we prove a new result for trees of large maximum degree, as well as some results for the cartesian power of a graph. We also make a conjecture about trees. |
| title | Some progress on $t$-tone coloring |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2510.13382 |