Abstract
Given a graph with edges colored Red and Blue, we wish to sample and approximately count the number of perfect matchings with exactly k Red edges. We study a Markov chain on the space of all matchings of a graph that favors matchings with k Red edges. We show that it is rapidly mixing using non-traditional canonical paths that can backtrack, based on an algorithm for a simple combinatorial problem. We show that this chain can be used to sample dimer configurations on a 2-dimensional toroidal region with k Red edges.
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Bhatnagar, N., Randall, D., Vazirani, V.V., Vigoda, E. (2006). Random Bichromatic Matchings. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_21
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DOI: https://doi.org/10.1007/11682462_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32755-4
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