Emergent Mind
Asymptotics of the chromatic number for quasi-line graphs
(1102.0805)
Published Feb 3, 2011
in
cs.DM
,
cs.DS
,
and
math.CO
Abstract
As proved by Kahn, the chromatic number and fractional chromatic number of a line graph agree asymptotically. That is, for any line graph $G$ we have $\chi(G) \leq (1+o(1))\chi_f(G)$. We extend this result to quasi-line graphs, an important subclass of claw-free graphs. Furthermore we prove that we can construct a colouring that achieves this bound in polynomial time, giving us an asymptotic approximation algorithm for the chromatic number of quasi-line graphs.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.