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A Note on the Stability Number of an Orthogonality Graph

Etienne de KlerkDimitrii PasechnikDmitrii V. Pasechnik

出版	Center for Economic Research, 2005
URL	http://books.google.com.hk/books?id=fbyTkQEACAAJ&hl=&source=gbs_api

註釋

We consider the orthoganality graph omega(n) with 2n vertices corresponding to the vectors {0,1}n, two vertices adjacent if and only if the Hamming distance between them is n/2. We show that, for n=16, the stability number of omega(n) is alpha(omega(16))=2304, thus proving a conjecture by Galliard [7]. The main tool we employ is a recent semidefinite programming relaxation for minimal distance binary codes due to Schrijver [16]. Moreover, we give a general condition for Delsarte bound on the (co)cliques in graphs of relations of association schemes to coincide with the ratio bound, and use it to show that for omega(n) the latter two bounds are equal 2n/n.