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A Note on First-Fit Coloring of Interval Graphs

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Abstract

We apply the Column Construction Method (Varadarajan et al., Proceedings of the Fifteenth Annual ACM-SIAM Symposium On Discrete Algorithms, pp. 562–571, 2004) to a minimal clique cover of an interval graph to obtain a new proof that First-Fit is 8-competitive for online coloring interval graphs. This proof also yields a new discovery that in each minimal clique cover of an interval graph G, there is a clique of size \(\frac{\omega(G)}{8}\).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology-Madras, Chennai, 600036, India

    N. S. Narayanaswamy & R. Subhash Babu

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  1. N. S. Narayanaswamy
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  2. R. Subhash Babu
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Correspondence to N. S. Narayanaswamy.

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Narayanaswamy, N.S., Babu, R.S. A Note on First-Fit Coloring of Interval Graphs. Order 25, 49–53 (2008). https://doi.org/10.1007/s11083-008-9076-6

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  • DOI: https://doi.org/10.1007/s11083-008-9076-6

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