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Hardness of Variants of the Graph Coloring Game

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LATIN 2020: Theoretical Informatics (LATIN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12118))

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Abstract

Very recently, a long-standing open question proposed by Bodlaender in 1991 was answered: the graph coloring game is PSPACE-complete. In 2019, Andres and Lock proposed five variants of the graph coloring game and left open the question of PSPACE-hardness related to them. In this paper, we prove that these variants are PSPACE-complete for the graph coloring game and also for the greedy coloring game, even if the number of colors is the chromatic number. Finally, we also prove that a connected version of the graph coloring game, proposed by Charpentier et al. in 2019, is PSPACE-complete.

R. Sampaio—Supported by CAPES [88887.143992/2017-00] DAAD Probral and [88881.197438/2018-01] STIC AmSud, CNPq Universal [401519/2016-3], [425297/2016-0] and [437841/2018-9], and FUNCAP [4543945/2016] Pronem.

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Authors and Affiliations

  1. Centro de Ciências e Tecnologia, University Federal do Cariri, Juazeiro do Norte, Brazil

    Thiago Marcilon

  2. University Integração Internacional Lusofonia Afrobrasileira Unilab, Redenção, Brazil

    Nicolas Martins

  3. Departamento de Computação, Universidade Federal do Ceará, Fortaleza, Brazil

    Rudini Sampaio

Authors
  1. Thiago Marcilon
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  2. Nicolas Martins
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  3. Rudini Sampaio
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Corresponding author

Correspondence to Rudini Sampaio .

Editor information

Editors and Affiliations

  1. University of São Paulo, São Paulo, Brazil

    Yoshiharu Kohayakawa

  2. University of Campinas, Campinas, Brazil

    Flávio Keidi Miyazawa

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Marcilon, T., Martins, N., Sampaio, R. (2020). Hardness of Variants of the Graph Coloring Game. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_28

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  • DOI: https://doi.org/10.1007/978-3-030-61792-9_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61791-2

  • Online ISBN: 978-3-030-61792-9

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