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Counting plane graphs: Perfect matchings, spanning cycles, and Kasteleyn's technique
2013
Journal of combinatorial theory. Series A
We derive improved upper bounds on the number of crossing-free straight-edge spanning cycles (also known as Hamiltonian tours and simple polygonizations) that can be embedded over any specific set of N points in the plane. More specifically, we bound the ratio between the number of spanning cycles (or perfect matchings) that can be embedded over a point set and the number of triangulations that can be embedded over it. The respective bounds are O (1.8181 N ) for cycles and O (1.1067 N ) for
doi:10.1016/j.jcta.2013.01.002
fatcat:u62vgjo7o5azthn7qbwjybgixm