@misc{StephanMaurrasNedev2010, author = {Stephan, R{\"u}diger and Maurras, Jean and Nedev, Roumen}, title = {On the connectivity of k-clique polytopes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11949}, number = {10-29}, year = {2010}, abstract = {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.}, language = {en} }