Sharp thresholds for constraint satisfaction problems and homomorphisms

Coarse and Sharp Thresholds of Boolean Constraint Satisfaction Problems

We study threshold properties of random constraint satisfaction problems under a probabilistic model due to Molloy [11]. We give a sufficient condition for the existence of a sharp threshold that leads (for boolean constraints) to a necessary and sufficient for the existence of a sharp threshold in the case where constraint templates are applied with equal probability, solving thus an open prob...

ar X iv : c s . D M / 0 50 30 83 v 1 2 9 M ar 2 00 5 Coarse and Sharp Thresholds of Boolean Constraint Satisfaction Problems ∗

We study threshold properties of random constraint satisfaction problems under a probabilistic model due to Molloy [11]. We give a sufficient condition for the existence of a sharp threshold that leads (for boolean constraints) to a necessary and sufficient for the existence of a sharp threshold in the case where constraint templates are applied with equal probability, solving thus an open prob...

Algorithmic aspects of graph homomorphisms

Homomorphisms are a useful model for a wide variety of combinatorial problems dealing with mappings and assignments, typified by scheduling and channel assignment problems. Homomorphism problems generalize graph colourings, and are in turn generalized by constraint satisfaction problems; they represent a robust intermediate class of problems – with greater modeling power than graph colourings, ...

Tractability of Constraint Satisfaction Problems and Projective Clone Homomorphisms

The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction

A signed graph (G,Σ) is an undirected graph G together with an assignment of signs (positive or negative) to all its edges, where Σ denotes the set of negative edges. Two signatures are said to be equivalent if one can be obtained from the other by a sequence of resignings (i.e. switching the sign of all edges incident to a given vertex). Extending the notion of usual graph homomorphisms, homom...