Recognizing halved cubes in a constant time per edge
نویسندگان
چکیده
منابع مشابه
A characterization of halved cubes
The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then it is proved that Qd is the only connected, ( d 2 ) -regular graph on 2d−1 vertices in which every edge lies in two d-cliques and two d-cliques do not intersect in a vertex.
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Let S be a family of subsets of a set X of cardinality m and VC-dim(S) be the Vapnik-Chervonenkis dimension of S. Haussler, Littlestone, and Warmuth (Inf. Comput., 1994) proved that if G1(S) = (V,E) is the subgraph of the hypercube Qm induced by S (called the 1-inclusion graph of S), then |E| |V | ≤ VC-dim(S). Haussler (J. Combin. Th. A, 1995) presented an elegant proof of this inequality using...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1995
ISSN: 0195-6698
DOI: 10.1016/0195-6698(95)90042-x