On combinatorial properties of spheres in eulidean spaces

Abstract

Let S d be the unit sphere in euclidean space Ed+ 1 with metric* 0. Let G = = ( V , E ) = (V(G), E(G)) be a graph. For 2 > 0 a 2-imbedding ~o o f G in S d is a 1 I mapp ing rp : V--* S d such tha t {x, y}~_ E if and only if O(qo(x), ¢p(y)) :>2. As there are no three points with pairwise distances bigger than ~ in any S d we get that no graph which contains… (More)
DOI: 10.1007/BF02579146

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