Mathematics – Combinatorics
Scientific paper
2011-02-04
Mathematics
Combinatorics
Scientific paper
We prove that $\chi(G) \leq \max {\omega(G), \Delta_2(G), (5/6)(\Delta(G) + 1)}$ for every graph $G$ with $\Delta(G) \geq 3$. Here $\Delta_2$ is the parameter introduced by Stacho that gives the largest degree that a vertex $v$ can have subject to the condition that $v$ is adjacent to a vertex whose degree is at least as large as its own. This upper bound generalizes both Brooks' Theorem and the Ore-degree version of Brooks' Theorem.
No associations
LandOfFree
An improvement on Brooks' Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An improvement on Brooks' Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An improvement on Brooks' Theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-52347