Abstract
Two classic "phase transitions" in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a random 2-SAT formula from satisfiable to unsatisfiable as the density of clauses increases. The random-graph result has been extended to the case of prescribed degree sequences, where the almost-sure nonexistence or existence of a giant component is related to a simple property of the degree sequence. We similarly extend the satisfiability result, by relating the almost-sure satisfiability or unsatisfiability of a random 2-SAT formula to an analogous property of its prescribed literal-degree sequence. The extension has proved useful in analyzing literal-degree-based algorithms for (uniform) random 3-SAT.
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Cooper, C., Frieze, A. & Sorkin, G. Random 2-SAT with Prescribed Literal Degrees. Algorithmica 48, 249–265 (2007). https://doi.org/10.1007/s00453-007-0082-7
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DOI: https://doi.org/10.1007/s00453-007-0082-7