Convexity in combinatorial structures
Duchet, Pierre
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Duchet, Pierre
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Joanna Cyman, Magdalena Lemańska, Joanna Raczek (2006)
Discussiones Mathematicae Graph Theory
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For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number of a...
Zyskowski, Janusz (2015-11-13T12:11:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Matematički Vesnik
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Josip E. Pečarić (1980)
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Siniša Vrećica (1981)
Publications de l'Institut Mathématique
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Taras Banakh, Ivan Hetman (2012)
Studia Mathematica
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A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...
H. R. Abdel-Gawad, D. K. Thomas (1991)
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Hüsseinov, F. (1999)
Journal of Convex Analysis
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Beiträge zur Algebra und Geometrie
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