On-line coloring \(k\)-colorable graphs
In this paper it is shown that for any \(k\), there exists an on-line algorithm that will colour any \(k\)-colourable graph on \(n\) vertices with \(O(n^{1-1/k!})\) colours, improving the previous bound of \(O(n\log^{(2k- 3)}n/\log^{(2k- 4)}n)\). For \(k= 3\) and \(k= 4\) it is possible to do even better.
scientific article; zbMATH DE number 1195643