Tangle and Ultrafilter: Game Theoretical Interpretation

Abstract

This paper extends the concept of filter on X into (Xf), where X is a finite underlying set and f is a symmetric submodular function from \(2^X\) to N. Then, we show a cryptomorphism between a free ultrafilter and co-tangle on (Xf). The paper also provides game-theoretical interpretations of a branch decomposition tree and a free ultrafilter on (Xf).

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Acknowledgements

This work was supported by JSPS KAKENHI Grant number 15K00007.

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Correspondence to Koichi Yamazaki.

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Fujita, T., Yamazaki, K. Tangle and Ultrafilter: Game Theoretical Interpretation. Graphs and Combinatorics 36, 319–330 (2020). https://doi.org/10.1007/s00373-019-02085-4

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Keywords

  • 05C83 Graph minors
  • 03G05 Boolean algebras
  • 54A20 Convergence in general topology