Improved deterministic online algorithms color k-colorable graphs with O(n to the power of 1 minus 1 over k(k-1)/2) colors for k at least 5 and O(n to the 14/17) for k=4, plus a randomized bound for bipartite graphs that narrows the gap to a factor of 1.09.
Effective coloration.The Journal of Symbolic Logic, 41(2):469–480
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Online Graph Coloring for $k$-Colorable Graphs
Improved deterministic online algorithms color k-colorable graphs with O(n to the power of 1 minus 1 over k(k-1)/2) colors for k at least 5 and O(n to the 14/17) for k=4, plus a randomized bound for bipartite graphs that narrows the gap to a factor of 1.09.