Ohba’s conjecture and beyond for generalized colorings
Let $G$ be a graph. Ohba's conjecture states that if $|V(G)|\leq 2\chi(G) +1$, then $\chi(G)=\chi^L(G)$. Noel, West, Wu and Zhu extended this result and proved that for any graph, $\chi^L(G)\leq\max\{\chi(G),\left\lceil(|V(G)+\chi(G)-1)/3\right\rceil\}$. Ohba, Kierstead and Noel proved that thi...
| Autor: | |
|---|---|
| Formato: | tesis de maestría |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/106757 |
| Acesso em linha: | https://hdl.handle.net/2117/106757 |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph theory List coloring Choosability Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | Let $G$ be a graph. Ohba's conjecture states that if $|V(G)|\leq 2\chi(G) +1$, then $\chi(G)=\chi^L(G)$. Noel, West, Wu and Zhu extended this result and proved that for any graph, $\chi^L(G)\leq\max\{\chi(G),\left\lceil(|V(G)+\chi(G)-1)/3\right\rceil\}$. Ohba, Kierstead and Noel proved that this bound is sharp for the ordinary chromatic number. In this work we prove that both results hold for generalized colorings as well, and find examples that prove the sharpness of the second one for the acyclic and star chromatic numbers. |
|---|