Journal of the Operations Research Society of China ›› 2019, Vol. 7 ›› Issue (2): 385-394.doi: 10.1007/s40305-019-00241-4

Special Issue: Discrete optimization

Previous Articles    

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

Peng-Fei Wan1,2, Xin-Zhuang Chen1   

  1. 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:2018-05-28 Revised:2018-10-24 Online:2019-06-30 Published:2019-06-30
  • Contact: Peng-Fei Wan, Xin-Zhuang Chen E-mail:pfwan@mail.nwpu.edu.cn;chenxzh8224@mail.nwpu.edu.cn
  • 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.

Key words: Spanning tree, Spanning forest, Bounded treewidth, Dynamic programming

CLC Number: