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Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs
The vertex-cover problem is studied for random graphs GN,cN having N vertices and cN edges. Exact numerical results are obtained by a branch-and-bound algorithm. It is found that a transition in the coverability at a c-dependent threshold x = xc(c) appears, where xN is the cardinality of the vertex cover. This transition coincides with a sharp peak of the typical numerical effort, which is need...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1952
ISSN: 0033-068X
DOI: 10.1143/ptp.8.1