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On the Number of Bases of Bicircular Matroids
Omer Giménez, Anna de Mier, and Marc Noy
Departament de Matem¨¤tica Aplicada II. Pau Gargallo 5, Universitat Polit¨¨cnica de Catalunya 08028 Barcelona, Spain
{omer.gimenez,anna.de.mier, marc.noy}@upc.es
Annals of Combinatorics 9 (1) p.35-45 March, 2005
AMS Subject Classification: 05B35, 05A16
Abstract:
Let t(G) be the number of spanning trees of a connected graph G, and let b(G) be the number of bases of the bicircular matroid
B(G). In this paper we obtain bounds relating b(G) and t(G), and study in detail the case where G is a complete graph Kn or a complete bipartite graph Kn,m.
Keywords: bicircular matroid, spanning tree, asymptotic enumeration

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