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The Game Chromatic Number of a Random Hypergraph

In: Discrete Mathematics and Applications

Author

Listed:
  • Debsoumya Chakraborti

    (Carnegie Mellon University)

  • Alan Frieze

    (Carnegie Mellon University)

  • Mihir Hasabnis

    (Carnegie Mellon University)

Abstract

We consider the following game, played on a k-uniform hypergraph H. There are q colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to color all the vertices and the other player, B, wishes to prevent this. The game chromatic number χ g(H) is the minimum number of colors for which A has a winning strategy. We consider this in the context of a random k-uniform hypergraph and prove upper and lower bounds that hold w.h.p.

Suggested Citation

  • Debsoumya Chakraborti & Alan Frieze & Mihir Hasabnis, 2020. "The Game Chromatic Number of a Random Hypergraph," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 153-175, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_6
    DOI: 10.1007/978-3-030-55857-4_6
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