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Asymptotic Thresholds for ( a : b ) Minimum-Degree Games

Author

Listed:
  • Adnane Fouadi

    (Laboratory of Engineering Science, Faculty of Science, Ibn Zohr University, Agadir 80000, Morocco)

  • Mourad El Ouali

    (Laboratory of Engineering Science, Faculty of Science, Ibn Zohr University, Agadir 80000, Morocco
    Department of Mathematics, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany)

  • Anand Srivastav

    (Department of Mathematics, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany)

Abstract

We investigate the ( a : b ) Maker–Breaker subgraph game played on the edge set of the complete graph K n , where n , a , b ∈ N , and Maker’s objective is to construct a member of a prescribed family of graphs H , while Breaker aims to prevent this. In our study, Breaker moves first, and H is taken to be either the family of connected spanning subgraphs or the family of spanning subgraphs with minimum-degree at least k = k ( n ) . For the ( a : b ) minimum-degree- k game, we determine the asymptotically optimal threshold bias across a wide range of values for a . For the ( a : b ) connectivity game, we resolve an open problem posed by Hefetz et al. (2012) by identifying the exact leading term in the asymptotic behavior of the threshold bias when a = c ln n .

Suggested Citation

  • Adnane Fouadi & Mourad El Ouali & Anand Srivastav, 2025. "Asymptotic Thresholds for ( a : b ) Minimum-Degree Games," Games, MDPI, vol. 16(5), pages 1-21, September.
    • Handle: RePEc:gam:jgames:v:16:y:2025:i:5:p:47-:d:1744368
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