A note on Reed's Conjecture about $\omega$, $\Delta$ and $\chi$ with respect to vertices of high degree

Vera Weil

Reed conjectured that for every graph, $\chi \le \lceil \frac{\Delta +\omega +1}{2}\rceil$ holds, where $\chi$, $\omega$ and $\Delta$ denote the chromatic number, clique number and maximum deg…