# Minimal vertex covers on finite-connectivity random graphs: a hard-sphere lattice-gas picture.

@article{Weigt2001MinimalVC, title={Minimal vertex covers on finite-connectivity random graphs: a hard-sphere lattice-gas picture.}, author={M. Weigt and A. Hartmann}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2001}, volume={63 5 Pt 2}, pages={ 056127 } }

The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapping to a lattice gas of hard spheres of (chemical) radius 1, and they are found to be in excellent agreement with numerical simulations. We give a detailed description of the replica-symmetric phase, including the size and entropy of the minimal vertex covers, and the structure of the unfrozen component which is found to percolate at a… Expand

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