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Decomposability of Abstract and Path-Induced Convexities in Hypergraphs

Francesco Mario Malvestuto, Marina Moscarini (2015)

Discussiones Mathematicae Graph Theory

An abstract convexity space on a connected hypergraph H with vertex set V (H) is a family C of subsets of V (H) (to be called the convex sets of H) such that: (i) C contains the empty set and V (H), (ii) C is closed under intersection, and (iii) every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by X and are not separated by any convex set that is a proper subset of X. A nonempty subset X of V (H) is...

Densité et dimension

Patrick Assouad (1983)

Annales de l'institut Fourier

Une partie 𝒮 de 2 X est appelée une classe de Vapnik-Cervonenkis si la croissance de la fonction Δ 𝒮 : r Sup { | A | | A X , | A | = r } est polynomiale; ces classes se trouvent être utiles en Statistique et en Calcul des Probabilités (voir par exemple Vapnik, Cervonenkis [V.N. Vapnik, A.YA. Cervonenkis, Theor. Prob. Appl., 16 (1971), 264-280], Dudley [R.M. Dudley, Ann. of Prob., 6 (1978), 899-929]).Le présent travail est un essai de synthèse sur les classes de Vapnik-Cervonenkis. Mais il contient aussi beaucoup de résultats nouveaux,...

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