# Professor Suohai Fan 8/13/2015

On $r$-hued colorings

of graphs

**Date:** 8/13/2015**Time:** 2:30PM-3:20PM**Place:** 315 Armstrong Hall

Suohai Fan

Abstract:For integers $k, r > 0$, a $(k, r )$-coloring of a graph $G$

is a proper $k$-coloring $c$ such that for any vertex $v$ with degree

$d(v)$, $v$ is adjacent to at least

min$\{d(v),r\}$ different colors. Such coloring is also called as an $r$-hued

coloring. The {\it $r$-hued chromatic number} of $G$, $\chi_{r}(G)$, is the least integer

$k$ such that a $(k, r )$-coloring of $G$ exists. In this talk, we will present some

of the progresses in this area.