# Online Coloring of Comparability Graphs: some results

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Publication date: 2007

We study online partitioning of posets from a graph theoretical point of view, which is coloring and cocoloring in comparability graphs. For the coloring problem, we analyse the First-Fit algorithm and show a ratio of $O(\sqrt{n})$; furthermore, we devise an algorithm with a competitivity ratio of $\frac{\chi+1}{2}$. For the cocoloring problem, we point out a tight bound of $\frac{n}{4} + \frac{1}{2}$ and we give better bounds in some more restricted cocoloring problems.

Keywords: Online ; Coloring ; Comparability Graphs ; Permutation Graphs Reference ROSE-REPORT-2007-001

Author: Demange, Marc; Leroy-Beaulieu, Benjamin

Source: https://infoscience.epfl.ch/record/102343?ln=en