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arXiv · 2101.01997

Counting independent sets in strongly orderable graphs

Marc Heinrich·Haiko Müller
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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 .

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Marc Heinrich, Haiko Müller. 2021-01-06. Counting independent sets in strongly orderable graphs. https://arxiv.org/abs/2101.01997

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