List-recoloring of two classes of planar graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911221962244096 |
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| author | Pan, Chenran Wang, Weifan Liu, Runrun |
| author_facet | Pan, Chenran Wang, Weifan Liu, Runrun |
| contents | For a graph $G$ with a list assignment $L$ and two $L$-colorings $α$ and $β$, an $L$-recoloring sequence from $α$ to $β$ is a sequence of proper $L$-colorings where consecutive colorings differ at exactly one vertex. We prove the existence of such a recoloring sequence in which every vertex is recolored at most a constant number of times under two conditions: (i) $G$ is planar, contains no $3$-cycles or intersecting $4$-cycles, and $L$ is a $6$-assignment; or (ii) the maximum average degree of $G$ satisfies $\mathrm{mad}(G) < \frac{5}{2}$ and $L$ is a $4$-assignment. These results strengthen two theorems previously established by Cranston. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | List-recoloring of two classes of planar graphs Pan, Chenran Wang, Weifan Liu, Runrun Combinatorics 05C For a graph $G$ with a list assignment $L$ and two $L$-colorings $α$ and $β$, an $L$-recoloring sequence from $α$ to $β$ is a sequence of proper $L$-colorings where consecutive colorings differ at exactly one vertex. We prove the existence of such a recoloring sequence in which every vertex is recolored at most a constant number of times under two conditions: (i) $G$ is planar, contains no $3$-cycles or intersecting $4$-cycles, and $L$ is a $6$-assignment; or (ii) the maximum average degree of $G$ satisfies $\mathrm{mad}(G) < \frac{5}{2}$ and $L$ is a $4$-assignment. These results strengthen two theorems previously established by Cranston. |
| title | List-recoloring of two classes of planar graphs |
| topic | Combinatorics 05C |
| url | https://arxiv.org/abs/2510.17628 |