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Asymptotics of the Chromatic Number for Quasi-Line Graphs


  • Contract grant sponsors: EBCO/Ebbich Postdoctoral Scholarship; NSERC Discovery Grants of Pavol Hell and Bojan Mohar (to A. D. K.); Canada Research Chair (to B. R.).


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 math formula. We extend this result to quasi-line graphs, an important subclass of claw-free graphs. Furthermore, we prove that we can construct a coloring that achieves this bound in polynomial time, giving us an asymptotic approximation algorithm for the chromatic number of quasi-line graphs