On the 3-colorability of triangle-free and fork-free graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913769514336256 |
|---|---|
| author | Schroeder, Joshua Wang, Zhiyu Yu, Xingxing |
| author_facet | Schroeder, Joshua Wang, Zhiyu Yu, Xingxing |
| contents | A graph $G$ is said to satisfy the Vizing bound if $χ(G)\leq ω(G)+1$, where $χ(G)$ and $ω(G)$ denote the chromatic number and clique number of $G$, respectively. It was conjectured by Randerath in 1998 that if $G$ is a triangle-free and fork-free graph, where the fork (also known as trident) is obtained from $K_{1,4}$ by subdividing two edges, then $G$ satisfies the Vizing bound. In this paper, we confirm this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10469 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the 3-colorability of triangle-free and fork-free graphs Schroeder, Joshua Wang, Zhiyu Yu, Xingxing Combinatorics 05C15, 05C17, 05C75 A graph $G$ is said to satisfy the Vizing bound if $χ(G)\leq ω(G)+1$, where $χ(G)$ and $ω(G)$ denote the chromatic number and clique number of $G$, respectively. It was conjectured by Randerath in 1998 that if $G$ is a triangle-free and fork-free graph, where the fork (also known as trident) is obtained from $K_{1,4}$ by subdividing two edges, then $G$ satisfies the Vizing bound. In this paper, we confirm this conjecture. |
| title | On the 3-colorability of triangle-free and fork-free graphs |
| topic | Combinatorics 05C15, 05C17, 05C75 |
| url | https://arxiv.org/abs/2111.10469 |