A counterexample to a conjecture of Laurent and Poljak

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dc.creatorDeza, Antoine
dc.creatorIndik, Gabriel
dc.date2005-12-21
dc.date.accessioned2026-07-07T06:55:37Z
dc.date.available2026-07-07T06:55:37Z
dc.descriptionThe 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.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0512493
dc.identifierhttp://arxiv.org/abs/math/0512493
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106337
dc.subjectCombinatorics
dc.subject90C27; 52B12
dc.titleA counterexample to a conjecture of Laurent and Poljak
dc.typetext

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