STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Uniform and minimal essential spanning forests on trees
Random Structures & Algorithms
The number of spanning trees of plane graphs with reflective symmetry
Journal of Combinatorial Theory Series A
Limits of dense graph sequences
Journal of Combinatorial Theory Series B
Growth of the number of spanning trees of the Erdős–Rényi giant component
Combinatorics, Probability and Computing
Identities and inequalities for tree entropy
Combinatorics, Probability and Computing
On the number of spanning trees a planar graph can have
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Enumeration of spanning trees of graphs with rotational symmetry
Journal of Combinatorial Theory Series A
Left and right convergence of graphs with bounded degree
Random Structures & Algorithms
Fast distributed computation in dynamic networks via random walks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Journal of the ACM (JACM)
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We give new formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular graphs. The general answer involves a quantity for infinite graphs that we call ‘tree entropy’, which we show is a logarithm of a normalized determinant of the graph Laplacian for infinite graphs. Tree entropy is also expressed using random walks. We relate tree entropy to the metric entropy of the uniform spanning forest process on quasi-transitive amenable graphs, extending a result of Burton and Pemantle [Ann. Probab. 21 1329–1371].