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Exploring the complexity boundary between coloring and list-coloring

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  • Flavia Bonomo
  • Guillermo Durán
  • Javier Marenco

Abstract

Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs where the former admits polynomial-time algorithms but the latter is NP-complete. Our goal is to analyze the computational complexity of coloring problems lying “between” (from a computational complexity viewpoint) these two problems: precoloring extension, μ-coloring, and (γ,μ)-coloring. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Flavia Bonomo & Guillermo Durán & Javier Marenco, 2009. "Exploring the complexity boundary between coloring and list-coloring," Annals of Operations Research, Springer, vol. 169(1), pages 3-16, July.
    • Handle: RePEc:spr:annopr:v:169:y:2009:i:1:p:3-16:10.1007/s10479-008-0391-5
    DOI: 10.1007/s10479-008-0391-5
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    Cited by:

    1. Markus Bohlin & Sara Gestrelius & Florian Dahms & Matúš Mihalák & Holger Flier, 2016. "Optimization Methods for Multistage Freight Train Formation," Transportation Science, INFORMS, vol. 50(3), pages 823-840, August.
    2. Trotta, Manuel & Archetti, Claudia & Feillet, Dominique & Quilliot, Alain, 2022. "Pickup and delivery problems with autonomous vehicles on rings," European Journal of Operational Research, Elsevier, vol. 300(1), pages 221-236.
    3. Leonardo Lamorgese & Carlo Mannino, 2015. "An Exact Decomposition Approach for the Real-Time Train Dispatching Problem," Operations Research, INFORMS, vol. 63(1), pages 48-64, February.
    4. Cláudia Linhares-Sales & Ana Maia & Nicolas Martins & Rudini Sampaio, 2014. "Restricted coloring problems on Graphs with few P 4 ’s," Annals of Operations Research, Springer, vol. 217(1), pages 385-397, June.

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