# Polynomial-Delay Enumeration of Monotonic Graph Classes

Jan Ramon, Siegfried Nijssen.

Year: 2009, Volume: 10, Issue: 33, Pages: 907−929

#### Abstract

Algorithms that list graphs such that no two listed graphs are isomorphic, are important building blocks of systems for mining and learning in graphs. Algorithms are already known that solve this problem efficiently for many classes of graphs of restricted topology, such as trees. In this article we introduce the concept of a dense augmentation schema, and introduce an algorithm that can be used to enumerate any class of graphs with polynomial delay, as long as the class of graphs can be described using a monotonic predicate operating on a dense augmentation schema. In practice this means that this is the first enumeration algorithm that can be applied theoretically efficiently in any frequent subgraph mining algorithm, and that this algorithm generalizes to situations beyond the standard frequent subgraph mining setting.