Cops and robbers on $P_5$-free graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911235309568000 |
|---|---|
| author | Chudnovsky, Maria Norin, Sergey Seymour, Paul Turcotte, Jérémie |
| author_facet | Chudnovsky, Maria Norin, Sergey Seymour, Paul Turcotte, Jérémie |
| contents | We prove that every connected $P_5$-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected $P_5$-free graph $G$ with independence number at least three contains a three-vertex induced path with vertices $a \hbox{-} b \hbox{-} c$ in order, such that every neighbour of $c$ is also adjacent to one of $a,b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cops and robbers on $P_5$-free graphs Chudnovsky, Maria Norin, Sergey Seymour, Paul Turcotte, Jérémie Combinatorics Discrete Mathematics 05C57 We prove that every connected $P_5$-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected $P_5$-free graph $G$ with independence number at least three contains a three-vertex induced path with vertices $a \hbox{-} b \hbox{-} c$ in order, such that every neighbour of $c$ is also adjacent to one of $a,b$. |
| title | Cops and robbers on $P_5$-free graphs |
| topic | Combinatorics Discrete Mathematics 05C57 |
| url | https://arxiv.org/abs/2301.13175 |