Abstract
We show that for anyk, there exists an on-line algorithm that will color anyk-colorable graph onn vertices withO(n1−1/k!) colors. This improves the previous best upper bound ofO(nlog(2k−3)n/log(2k−4)n) due to Lovasz, Saks, and Trotter. In the special casesk=3 andk=4 we obtain on-line algorithms that useO(n2/3log1/3n) andO(n5/6log1/6n) colors, respectively.
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