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A counterexample to a conjecture of Laurent and Poljak | | Antoine Deza
; Gabriel Indik
; | | Date: |
21 Dec 2005 | | Subject: | Combinatorics | | 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 Laurent-Poljak conjecture, we exhibit a fractional vertex not adjacent to any integral vertex. | | Source: | arXiv, math/0512493 | | Services: | Forum | Review | PDF | Favorites | |
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