Computing the Number of k-Component Spanning Forests of a Graph with Bounded Treewidth

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  • 1 Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710029, China;
    2 School of Mathematics and Statistics, Yulin University, Yulin 719000, Shaanxi, China

Received date: 2018-05-28

  Revised date: 2018-10-24

  Online published: 2019-06-30

Supported by

This research was supported by the National Natural Science Foundation of China (Nos. 11571135, 11671320 and 11601430).

Abstract

Let G be a graph on n vertices with bounded treewidth. We use fk(G) to denote the number of spanning forests of G with k components. Given a tree decomposition of width at most p of G, we present an algorithm to compute fk(G) for k=1, 2,…, n. The running time of our algorithm is O((B(p + 1))3 pn3), where B(p + 1) is the (p + 1)-th Bell number.

Cite this article

Peng-Fei Wan, Xin-Zhuang Chen . Computing the Number of k-Component Spanning Forests of a Graph with Bounded Treewidth[J]. Journal of the Operations Research Society of China, 2019 , 7(2) : 385 -394 . DOI: 10.1007/s40305-019-00241-4

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