Inhomogeneous Hypergraphs

lie de Panafieu

Jeudi 02 juillet 2015 à 11h, salle 24-25/405


We introduce the inhomogeneous hypergraph model. Each edge can contain an arbitrary number of vertices, the vertices are colored, and each edge receives a weight which depends on the colors of the vertices it contains. This model provides a uniform setting to solve problems arising from various domains of computer science and mathematics. We will focus on applications to the enumeration of satisfied and satisfiable instances of Constraint Satisfaction Problems (CSP), and compute the limit probability for a random graph to be bipartit, the limit probability of satisfiability of systems of equations, the enumeration of properly k-colored graphs and investigate some graphs coming from social networks. We will present results on the asymptotics of inhomogeneous hypergraphs and their typical structure. Our main tool is analytic combinatorics.