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Communicated by the Editors
, 1977
"... In the paper a short proof is given for Kneser’s conjecture. The proof is based on Borsuk’s theorem and on a theorem of Gale. Recently, LOV~SZ has given a proof for Kneser’s conjecture [4]. He used Borsuk’s theorem. This fact gave the author the idea of the proof we present here. THEOREM (Kneser’s c ..."
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In the paper a short proof is given for Kneser’s conjecture. The proof is based on Borsuk’s theorem and on a theorem of Gale. Recently, LOV~SZ has given a proof for Kneser’s conjecture [4]. He used Borsuk’s theorem. This fact gave the author the idea of the proof we present here. THEOREM (Kneser’s
whl2224.tmp
"... Abstract In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomialsize) LP relaxations in place of exponentialsize models requiring separation algorithms. In the same vein as a celebrated theorem by Grotschel, Lov&sz and Schrijver, we state the e ..."
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Abstract In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomialsize) LP relaxations in place of exponentialsize models requiring separation algorithms. In the same vein as a celebrated theorem by Grotschel, Lov&sz and Schrijver, we state
Directed st Numberings, Rubber Bands, and Testing Digraph kVertex Connectivity
"... Let G = (V, E) be a directed graph and n denote V. We show that G is kvertex connected iff for every subset X of V with IX I = k, there is an embedding of G in the (k I)dimensional space Rkl, ~ : V ~Rkl, such that no hyperplane contains k points of {~(v) \ v G V}, and for each v E V – X, f( ..."
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Cited by 12 (1 self)
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(v) is in the convex hull of {~(w) I (v, W) G E}. This result generalizes to directed graphs the notion of convex embedding of undirected graphs introduced by Linial, LOV6SZ and Wigderson in ‘Rubber bands, convex embedding and graph connectivity, ” Combinatorics 8 (1988), 91102. Using this characterization, a
DESIGN CONCEPTS FOR MATRICES AND LATTICES IN I_iDIA
"... In this paper we present a new template class concept for matrices and lattices. In the design we have focussed on the efficiency of single as well as sequences of operations. In order to get concise and efficient programming code we present a new technique based on template mechanisms and suitable ..."
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In this paper we present a new template class concept for matrices and lattices. In the design we have focussed on the efficiency of single as well as sequences of operations. In order to get concise and efficient programming code we present a new technique based on template mechanisms and suitable inheritance structures. 1