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
        }
}
  • M. Weigt, A. Hartmann
  • Published 2001
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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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