Counting Spanning Trees ∗

This book provides a comprehensive introduction to the modern study of spanning trees. A spanning tree for a graph G is a subgraph of G that is a tree and contains all the vertices of G. There are many situations in which good spanning trees must be found. Whenever one wants to find a simple, cheap, yet efficient way to connect a set of terminals, be they computers, telephones, factories, or cities, a solution is normally one kind of spanning trees. Spanning trees prove important for several reasons:

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