5
votes
Algorithms to count perfect matchings in near planar graphs
Graphs of bounded genus (both orientable or non-orientable):
G. Tesler, Matchings in Graphs on Non-orientable Surfaces, Journal of Combinatorial Theory, Series B,
Volume 78, Issue 2 (2000), 198-231.
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1
vote
Which are good algorithms for finding Hamiltonian path (not necessarily a circle) up to now?
For random graphs, there are algorithms that are efficient on average. See for example A fast algorithm on average for solving the Hamilton Cycle problem by Michael Anastos and the references therein.
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