The birth of the contradictory component in random 2-SAT [article]

Sergey Dovgal
2019 arXiv   pre-print
We prove that, with high probability, the contradictory components of a random 2-SAT formula in the subcritical phase of the phase transition have only 3-regular kernels. This follows from the relation between these kernels and the complex component of a random graph in the subcritical phase. This partly settles the question about the structural similarity between the phase transitions in 2-SAT and random graphs. As a byproduct, we describe the technique that allows to obtain a full asymptotic
more » ... xpansion of the satisfiability in the subcritical phase. We also obtain the distribution of the number of contradictory variables and the structure of the spine in the subcritical phase.
arXiv:1904.10266v1 fatcat:4inbubamozcizamt65w5qyp5jq