TY - GEN A1 - Stephan, RĂ¼diger A1 - Maurras, Jean A1 - Nedev, Roumen T1 - On the connectivity of k-clique polytopes N2 - 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. T3 - ZIB-Report - 10-29 KW - clique polytope KW - connectivity Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11949 ER -