# 澳门新葡新京,澳门新葡新京官方网站

r-hued coloring of P_t free graphs

(i) If $G$ is a $P_4$-free graph, then $\chi_r(G)\leq \chi(G)+2(r-1)$, and this bound is best possible.

(ii) If $G$ is a $P_5$-free bipartite graph, then $\chi_r(G)\le r\chi(G)$, and this bound is best possible.

(iii) If $G$ is a $P_5$-free graph, then $\chi_2(G)\le 2\chi(G)$, and this bound is best possible.