A Dichotomy for 2-Constraint Forbidden CSP Patterns
  Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach has recently led to the discovery of novel tractable classes. The complete characterisation of all tractable classes defined by forbidding patterns (where a pattern is simply a compact representation of a set of subproblems) is a challenging problem. We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints. This has allowed us to discover new tractable classes including, for example, a novel generalisation of 2SAT. 
Martin C. Cooper and Guillaume Escamocher
cs.AI cs.CC