List-$k$-Coloring $H$-free graphs for all $k>4$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915228406513664 |
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| author | Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie |
| author_facet | Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie |
| contents | Given an integer $k>4$ and a graph $H$, we prove that, assuming P$\neq$NP, the List-$k$-Coloring Problem restricted to $H$-free graphs can be solved in polynomial time if and only if either every component of $H$ is a path on at most three vertices, or removing the isolated vertices of $H$ leaves an induced subgraph of the five-vertex path. In fact, the "if" implication holds for all $k\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05713 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | List-$k$-Coloring $H$-free graphs for all $k>4$ Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie Combinatorics Given an integer $k>4$ and a graph $H$, we prove that, assuming P$\neq$NP, the List-$k$-Coloring Problem restricted to $H$-free graphs can be solved in polynomial time if and only if either every component of $H$ is a path on at most three vertices, or removing the isolated vertices of $H$ leaves an induced subgraph of the five-vertex path. In fact, the "if" implication holds for all $k\geq 1$. |
| title | List-$k$-Coloring $H$-free graphs for all $k>4$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2311.05713 |