Total coloring graphs with large minimum degree
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909678950154240 |
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| author | Henderschedt, Owen McDonald, Jessica Shan, Songling |
| author_facet | Henderschedt, Owen McDonald, Jessica Shan, Songling |
| contents | We prove that for all $\varepsilon>0$, there exists a positive integer $n_0$ such that if $G$ is a graph on $n\geq n_0$ vertices with $δ(G)\geq\tfrac{1}{2}(1 + \varepsilon)n$, then $G$ satisfies the Total Coloring Conjecture, that is, $χ_T(G)\leq Δ(G)+2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Total coloring graphs with large minimum degree Henderschedt, Owen McDonald, Jessica Shan, Songling Combinatorics 05C15 We prove that for all $\varepsilon>0$, there exists a positive integer $n_0$ such that if $G$ is a graph on $n\geq n_0$ vertices with $δ(G)\geq\tfrac{1}{2}(1 + \varepsilon)n$, then $G$ satisfies the Total Coloring Conjecture, that is, $χ_T(G)\leq Δ(G)+2$. |
| title | Total coloring graphs with large minimum degree |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2507.05548 |