Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
On Properties of a Set of Global Roundings Associated with Clique Connection of Graphs
Tomonori ISHIKAWAKen-ich KAWARABAYASHITakeshi TOKUYAMA
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2004 Volume 10 Issue 2 Pages 159-163

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Abstract

Given a connected weighted graph G=(V,E), we consider a hypergraph H(G)=(V,F(G)) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding α with respect to H(G) is a binary assignment satisfying that |∑vFa(v)−α(v)|<1 for every FF(G). Asano et al. [3] conjectured that there are at most |V|+1 global roundings for H(G). In this paper, we present monotone properties on size and affine corank of a set of global roundings under a clique connection operation.

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© 2004 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
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