## Abstract

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning of T is a subset R of the rooms such that each vertex of T is in exactly one room in R.We prove that if T has a room-partitioning R, then there is another room-partitioning of T which is different from R. The proof is a simple algorithm which walks from room to room, which however we show to be exponential by constructing a sequence of (planar) instances, where the algorithm walks from room to room an exponential number of times relative to the number of rooms in the instance.We unify the above theorem with Nash's theorem stating that a 2-person game has an equilibrium, by proving a combinatorially simple common generalization.

Original language | English |
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Pages (from-to) | 1257-1264 |

Number of pages | 8 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 36 |

Issue number | C |

DOIs | |

Publication status | Published - Aug 2010 |

Externally published | Yes |

## Keywords

- 2-person games
- Exchange algorithm
- Room-partitioning