Summary
I shall discuss some of the more well known counting problems associated with graphs and matroids. Except in special cases all these problems have no exact counting algorithm which runs in polynomial time unless there is a remarkable collapse of some existing classes. Hence the focus is on obtaining fast algorithms which give good approximations. The problems studied include counting forests, trees and colourings of graphs and bases of matroids.
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Welsh, D. (2009). Some Problems on Approximate Counting in Graphs and Matroids. In: Cook, W., Lovász, L., Vygen, J. (eds) Research Trends in Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76796-1_23
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