Stones, Rebecca, - Computing the number of h-edge spanning forests in complete bipartite graphs

dmtcs:1248 - Discrete Mathematics & Theoretical Computer Science, May 12, 2014, Vol. 16 no. 1 (in progress)
Computing the number of h-edge spanning forests in complete bipartite graphs

Authors: Stones, Rebecca,

Let fm,n,h be the number of spanning forests with h edges in the complete bipartite graph Km,n. Kirchhoff\textquoterights Matrix Tree Theorem implies fm,n,m+n-1=mn-1 nm-1 when m ≥1 and n ≥1, since fm,n,m+n-1 is the number of spanning trees in Km,n. In this paper, we give an algorithm for computing fm,n,h for general m,n,h. We implement this algorithm and use it to compute all non-zero fm,n,h when m ≤50 and n ≤50 in under 2 days.


Source : oai:HAL:hal-01179216v1
Volume: Vol. 16 no. 1 (in progress)
Section: Analysis of Algorithms
Published on: May 12, 2014
Submitted on: October 6, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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