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

Phys Rev E Stat Nonlin Soft Matter Phys

Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.

Published: December 2004

Vertex cover is one of the classical NP-complete problems in theoretical computer science. A vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset. When studied on Erdo s-Re nyi random graphs (with connectivity c) one observes a threshold behavior: In the thermodynamic limit the size of the minimal vertex cover is independent of the specific graph. Recent analytical studies show that on the phase boundary, for small connectivities c

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