Cliques and High Odd Holes in Graphs with Chromatic Number Equal to Maximum Degree
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908487974387712 |
|---|---|
| author | Galindo, Rachel McDonald, Jessica Shan, Songling |
| author_facet | Galindo, Rachel McDonald, Jessica Shan, Songling |
| contents | We give a uniform and self-contained proof that if $G$ is a connected graph with $χ(G) = Δ(G)$ and $G\neq \overline{C_7}$, then $G$ contains either $K_{Δ(G)}$ or an odd hole where every vertex has degree at least $Δ(G)-1$ in $G$. This was previously proved in series of two papers by Chen, Lan, Lin, and Zhou, who used the Strong Perfect Graph Theorem for the cases $Δ(G)=4, 5, 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cliques and High Odd Holes in Graphs with Chromatic Number Equal to Maximum Degree Galindo, Rachel McDonald, Jessica Shan, Songling Combinatorics We give a uniform and self-contained proof that if $G$ is a connected graph with $χ(G) = Δ(G)$ and $G\neq \overline{C_7}$, then $G$ contains either $K_{Δ(G)}$ or an odd hole where every vertex has degree at least $Δ(G)-1$ in $G$. This was previously proved in series of two papers by Chen, Lan, Lin, and Zhou, who used the Strong Perfect Graph Theorem for the cases $Δ(G)=4, 5, 6$. |
| title | Cliques and High Odd Holes in Graphs with Chromatic Number Equal to Maximum Degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.02939 |