Maker Breaker on Digraphs

Alan Frieze; Wesley Pegden

Maker Breaker on Digraphs

Combinatorics 2021-12-01 v4

Authors: Alan Frieze , Wesley Pegden

Abstract

We study two biassed Maker-Breaker games played on the complete digraph $\vec{K}_n$ . In the strong connectivity game, Maker wants to build a strongly connected subgraph. We determine the asymptotic optimal bias for this game viz. $\frac{n}{\log n}$ . In the Hamiltonian game, Maker wants to build a Hamiltonian subgraph. We determine the asymptotic optimal bias for this game up to a constant factor.

Keywords

combinatorial game theory

Cite

@article{arxiv.2003.13521,
  title  = {Maker Breaker on Digraphs},
  author = {Alan Frieze and Wesley Pegden},
  journal= {arXiv preprint arXiv:2003.13521},
  year   = {2021}
}

Comments

We clarify an important argument in the appendix

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