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On transitivity of proximinality

โœ Scribed by V Indumathi


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
683 KB
Volume
49
Category
Article
ISSN
0021-9045

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We examine edge transitivity of directed graphs. The class of local comparability graphs is defined as the underlying graphs of locally edge transitive digraphs. The latter generalize edge transitive orientations, while local comparability graphs include comparability, anticomparability, and circle

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We say that a normed linear space X is a R(1) space if the following holds: If Y is a closed subspace of finite codimension in X and every hyperplane containing Y is proximinal in X then Y is proximinal in X. In this paper we show that any closed subspace of c 0 is a R(1) space. ## 1999 Academic Pr

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In this paper we investigate the foliowing generalization of transitivity: A digraph D is (m, n)-transitive whenever there is a path of length m from x to y there is a subset of n + 1 vertices of these m + 1 vertices which contain a path of length n from x to y. Here we study various properties of