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The second neighborhood conjecture of Seymour asserts that for any orientation G = (V, E), there exists a vertex v ∈ V so that |N + (v)| ≤ |N ++ (v)|. The conjecture was resolved by Fisher for tournaments. In this paper we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results,(More)
To assess the prevalence of macrocephaly (head circumference > or = 1.88 standard deviations above normative data for age and sex or > 97th centile) in autism and other pervasive developmental disorders, 41 children with autism, and a comparison group of 21 children with tuberous sclerosis complex (TSC) or an unspecified seizure disorder were studied.(More)
A k-majority tournament is realized by 2k −1 linear orders on the set of vertices, where a vertex u dominates v if u precedes v in at least k of the orders. Various properties of such tournaments have been studied, among them the problem of finding the size of a smallest dominating set. It is known that 2-majority tournaments are dominated by 3 vertices and(More)
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