# Random Necklaces, Graphs and Molecules: The Challenge of Unlabelled Sampling

## Leslie Goldberg

## Abstract

Informally, an "unlabelled combinatorial structure" is an object such
as an unlabelled graph (in which the vertices are indistinguishable)
or a structural isomer in chemistry (which shows how the various atoms
of a molecule should be connected, without further distinguishing
between different atoms of the same type). This talk is concerned
with the question ``How do you sample uniformly at random from a set
of unlabelled combinatorial structures?'' The talk will survey known
algorithmic methods which apply to such problems, and will point out
limitations of the known methods. Some of the many open problems in this
area will be discussed.