The square of every subcubic planar graph of girth at least 6 is 7-choosable
| Autor: | Kim, Seog-Jin, Lian, Xiaopan |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Thomassen (2018) and Hartke, Jahanbekam and Thomas (2016) proved that $\chi(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is whether $\chi_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph. Cranston and Kim (2008) showed that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 7. We prove that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 6. Comment: 9 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|