Displaying similar documents to “Convex domination in the composition and Cartesian product of graphs”

Graphs with convex domination number close to their order

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 d G ( u , v ) between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length d G ( u , v ) 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 γ c o n ( G ) of a...

A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

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 C o n v ( X ) of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...