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Total Version of the Domination Game

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Abstract

In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.

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Acknowledgments

Research supported in part by the South African National Research Foundation and the University of Johannesburg, by the Ministry of Science of Slovenia under the Grants P1-0297, and by a Grant from the Simons Foundation (#209654 to Douglas Rall) and by the Wylie Enrichment Fund of Furman University. We thank the referees for several useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Johannesburg, Johannesburg, South Africa

    Michael A. Henning

  2. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Sandi Klavžar

  3. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Sandi Klavžar

  4. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Sandi Klavžar

  5. Department of Mathematics, Furman University, Greenville, SC, USA

    Douglas F. Rall

Authors
  1. Michael A. Henning
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  2. Sandi Klavžar
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  3. Douglas F. Rall
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Correspondence to Sandi Klavžar.

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Henning, M.A., Klavžar, S. & Rall, D.F. Total Version of the Domination Game. Graphs and Combinatorics 31, 1453–1462 (2015). https://doi.org/10.1007/s00373-014-1470-9

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  • DOI: https://doi.org/10.1007/s00373-014-1470-9

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