Counting independent sets in strongly orderable graphs

TL;DR

This paper presents polynomial-time algorithms for counting independent sets in strongly orderable graphs and graphs of bounded clique-width, extending to weighted and size-specific cases.

Contribution

It introduces new polynomial-time algorithms for counting independent sets in strongly orderable graphs and bounded clique-width graphs, expanding the classes of graphs with efficient counting methods.

Findings

Polynomial-time algorithm for strongly orderable graphs

Algorithm extends to weighted graphs and fixed size k

Applicable to graphs of bounded clique-width

Abstract

We consider the problem of devising algorithms to count exactly the number of independent sets of a graph G . We show that there is a polynomial time algorithm for this problem when G is restricted to the class of strongly orderable graphs, a superclass of chordal bipartite graphs. We also show that such an algorithm exists for graphs of bounded clique-width. Our results extends to a more general setting of counting independent sets in a weighted graph and can be used to count the number of independent sets of any given size k .