A note on random 2-SAT with prescribed literal degrees

Authors:
Colin Cooper;Alan Frieze;Gregory B. Sorkin
Affiliations:
University of London, London SE14 6NW, UK;Carnegie Mellon University, Pittsburgh PA;IBM T.J. Watson Research Center, Yorktown Heights NY
Venue:
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2002

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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 a prescribed literal sequence.