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 graph $G$, let $\chi(G)$ ($\omega(G)$) denote its chromatic (clique)number. A $P_2+P_3$ is the graph obtained by taking the disjoint union of atwo-vertex path $P_2$ and a three-vertex path $P_3$. A $\bar{P_2+P_3}$ is thecomplement graph of a $P_2+P_3$. In this paper, we study the class of($P_2+P_3$, $\bar{P_2+P_3}$)-free graphs and show that every such graph $G$with $\omega(G)\geq 3$ satisfies $\chi(G)\leq \max \{\omega(G)+3,\lfloor\frac{3}{2} \omega(G) \rfloor-1 \}$. Moreover, the bound is tight.Indeed, for any $k\in {\mathbb N}$ and $k\geq 3$, there is a ($P_2+P_3$,$\bar{P_2+P_3}$)-free graph $G$ such that $\omega(G)=k$ and $\chi(G)=\max\{k+3,\lfloor\frac{3}{2} k \rfloor-1 \}$.

Optimal chromatic bound for ($P_2+P_3$, $\bar{P_2+ P_3}$)-free graphs