Sharp thresholds for constraint satisfaction problems and homomorphisms

TL;DR

This paper identifies conditions under which various models of random constraint satisfaction problems exhibit sharp thresholds of satisfiability, enhancing understanding of phase transitions in these problems.

Contribution

It provides a comprehensive analysis of sharp thresholds across multiple models including graph homomorphisms, hypergraph models, and small domain CSPs, which was previously less understood.

Findings

Sharp thresholds established for graph and hypergraph homomorphisms

Conditions identified for the existence of sharp thresholds in the $(d,k,t)$-model

Analysis extended to binary CSPs with domain size three

Abstract

We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary constraint satisfaction problems with domain size three.