Some Problems on Approximate Counting in Graphs and Matroids

Dominic Welsh ()
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Dominic Welsh: University of Oxford, Mathematical Institute

Chapter 23 in Research Trends in Combinatorial Optimization, 2009, pp 523-544 from Springer

Abstract: 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.

Date: 2009
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DOI: 10.1007/978-3-540-76796-1_23

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