A counterexample to the dominating set conjecture

Antoine Deza (dezamcmaster.ca)
Gabriel Indik (indikgmcmaster.ca)

Abstract: The metric polytope m(n) is the polyhedron associated with all semimetrics on n nodes. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n<9 and, in particular, for the 1 550 825 600 vertices of m(8). While the overwhelming majority of the known vertices of m(9) satisfy the conjecture, we exhibit a fractional vertex not adjacent to any integral vertex.

Keywords: Dominating Set Conjecture, Metric polyhedra, Cut polyhedra

Category 1: Combinatorial Optimization

Category 2: Combinatorial Optimization (Polyhedra )

Citation: AdvOL-Report 2005/21, McMaster University, Hamilton, Ontario, Canada (November 2005)

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Entry Submitted: 12/21/2005
Entry Accepted: 12/21/2005
Entry Last Modified: 04/01/2006

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