Weakly pancyclic vertices in dense nonbipartite graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908781419429888 |
|---|---|
| author | Tang, Yurui Zhan, Xingzhi |
| author_facet | Tang, Yurui Zhan, Xingzhi |
| contents | Let $G$ be a graph of girth $g$ and circumference $c.$ A vertex $v$ of $G$ is called weakly pancyclic if $v$ lies on an $\ell$-cycle for every integer $\ell$ with $g\le \ell\le c.$ We prove that if $G$ is a nonbipartite graph of order $n\ge 5$ and size at least $\left\lfloor(n-1)^2/4\right\rfloor+2,$ then $G$ contains three weakly pancyclic vertices, with one exception. This strengthens a result of Brandt from 1997. We also pose a related problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weakly pancyclic vertices in dense nonbipartite graphs Tang, Yurui Zhan, Xingzhi Combinatorics Let $G$ be a graph of girth $g$ and circumference $c.$ A vertex $v$ of $G$ is called weakly pancyclic if $v$ lies on an $\ell$-cycle for every integer $\ell$ with $g\le \ell\le c.$ We prove that if $G$ is a nonbipartite graph of order $n\ge 5$ and size at least $\left\lfloor(n-1)^2/4\right\rfloor+2,$ then $G$ contains three weakly pancyclic vertices, with one exception. This strengthens a result of Brandt from 1997. We also pose a related problem. |
| title | Weakly pancyclic vertices in dense nonbipartite graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.15822 |