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Keyword: connectivity threshold ×Clear all

2 claims from 1 paper

1. Physics and Astronomy › Theoretical and Computational Physics

   Clustering analysis of the ground-state structure of the vertex-cover problem

   Barthel and Hartmann · Physical Review E · 2004

   The authors numerically studied the structure of minimal vertex-cover solutions on random graphs, to compare with analytical predictions of a change in behaviour at connectivity c=e.

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   1. UncheckedThe paper's numerical analyses of vertex-cover solutions on random graphs are all compatible with a structural change at connectivity c=e.“All results are compatible with a change at c=e.”
   2. UncheckedOn random graphs, vertex-cover solutions form few clusters at low connectivity, but cluster numbers slowly grow with system size at higher connectivity.“For small connectivities, the solutions are collected in a finite small number of clusters, while the number of cluster diverges slowly with system size for larger connectivities and replica symmetry breaking, but not 1-RSB, occurs.”