English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family ofgraphs which have girth $2\ell+1$ and have no odd hole with length greater than$2\ell+1$. Plummer and Zha conjectured that every 3-connected and internally4-connected graph in $\mathcal{G}_2$ is 3-colorable. Wu, Xu, and Xu conjecturedthat every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable.Chudnovsky et al. and Wu et al., respectively, proved that every graph in$\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we provethat every graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ is 3-colorable.

Graphs with girth $2\ell+1$ and without longer odd holes are $3$-colorable