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On the connectivity of k-clique polytopes

Please always quote using this URN: urn:nbn:de:0297-zib-11949
  • In this paper, we study the neighbourlicity of the polytope $P_{k n}^2$ constituted by the $k$-cliques of the complete graph $K_n$ on $n$ vertices. We prove that this polytope is $3$-, but not $4$-neighbourly. Following a remark of Pierre Duchet, we partially generalize this result to the $k$-clique polytopes of $r$-uniform complete hypergraphs, $P_{kn}^r$. We show that the neighbourlicity of $P_{kn}^r$ is between $r$ and $2^r-1$ whenever $k\geq r+1$ and $n\geq k+r+1$. Computational results indicate that the upper bound is tight.

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Metadaten
Author:Rüdiger Stephan, Jean Maurras, Roumen Nedev
Document Type:ZIB-Report
Tag:clique polytope; connectivity
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Date of first Publication:2010/12/22
Series (Serial Number):ZIB-Report (10-29)
ZIB-Reportnumber:10-29
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