Sudden emergence of q-regular subgraphs in random graphs
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We investigate the computationally hard problem whether a random graph of finite average vertex degree has an extensively large q-regular subgraph, i.e., a subgraph with all vertices having degree equal to q. We reformulate this problem as a constraint-satisfaction problem, and solve it using the cavity method of statistical physics at zero temperature. For q = 3, we find that the first large q-regular subgraphs appear discontinuously at an average vertex degree c3 − reg 3.3546 and contain immediately about 24% of all vertices in the graph. This transition is extremely close to (but different from) the well-known 3-core percolation point c3 − core 3.3509. For q > 3, the q-regular subgraph percolation threshold is found to coincide with that of the q-core.
[1] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[2] Riccardo Zecchina,et al. Coloring random graphs , 2002, Physical review letters.
[3] Ericka Stricklin-Parker,et al. Ann , 2005 .
[4] Cristopher Moore,et al. Computational Complexity and Statistical Physics , 2006, Santa Fe Institute Studies in the Sciences of Complexity.