Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.
Exact sampling with coupled Markov chains and applications to statistical mechanics.Random Structures & Algorithms, 9(1-2):223– 252, 1996
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Graph Disjointness with Applications to Reversible Markov Chains
Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.