On finding another room-partitioning of the vertices

Jack Edmonds, Laura Sanità

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)1257-1264
Number of pages8
JournalElectronic Notes in Discrete Mathematics
Issue numberC
Publication statusPublished - Aug 2010
Externally publishedYes


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


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