# Discrete Mathematics Seminar: Constructing, sampling and counting graphical realizations of restricted degree sequences

Speaker: Peter Erdos

Renyi Institute, Budapest

With the current burst of network theory research (especially in connection with social and biological networks) there is a renewed interest on realiza6ons of given degree sequences and uniform sampling of those realizations. In this lecture we propose a new degree

sequence problem: we want to find graphical realizations of a given degree sequence on labeled vertices, where certain wouldbe edges are forbidden. Then we want to sample uniformly all possible realizations.

Originally published at math.nd.edu.