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Inverse chromatic number problems in interval and permutation graphs

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  • Chung, Yerim
  • Culus, Jean-François
  • Demange, Marc

Abstract

Given a graph G and a positive integer K, the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than K. In this paper, we focus on the inverse chromatic number problem for certain classes of graphs. First, we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs: the inverse booking problem and the inverse track assignment problem. The inverse booking problem is closely related to some previously known scheduling problems; we propose new hardness results and polynomial cases. The inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs; we show how to solve in polynomial time a generalization of the problem with a bounded number of colors.

Suggested Citation

  • Chung, Yerim & Culus, Jean-François & Demange, Marc, 2015. "Inverse chromatic number problems in interval and permutation graphs," European Journal of Operational Research, Elsevier, vol. 243(3), pages 763-773.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:3:p:763-773
    DOI: 10.1016/j.ejor.2014.12.028
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    1. Jianzhong Zhang & Mao Cai, 1998. "Inverse problem of minimum cuts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 51-58, February.
    2. de Werra, D., 1996. "Extensions of coloring models for scheduling purposes," European Journal of Operational Research, Elsevier, vol. 92(3), pages 474-492, August.
    3. Demange, Marc & Ekim, Tınaz & Ries, Bernard & Tanasescu, Cerasela, 2015. "On some applications of the selective graph coloring problem," European Journal of Operational Research, Elsevier, vol. 240(2), pages 307-314.
    4. Demange, Marc & Ekim, TInaz & de Werra, Dominique, 2009. "A tutorial on the use of graph coloring for some problems in robotics," European Journal of Operational Research, Elsevier, vol. 192(1), pages 41-55, January.
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    Cited by:

    1. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    2. Tınaz Ekim & Mordechai Shalom & Oylum Şeker, 2021. "The complexity of subtree intersection representation of chordal graphs and linear time chordal graph generation," Journal of Combinatorial Optimization, Springer, vol. 41(3), pages 710-735, April.

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