Slightly later, and less formally published reference than David E.'s citation:

> Sharir, Micha, Adam Sheffer, and Emo Welzl. "Counting plane graphs: Perfect matchings, spanning cycles, and Kasteleyn's technique." *Proceedings 28th Symposium on Computational Geometry*. ACM, 2012.

>[...] a new upper bound of $O(54.5^N)$ on the number of crossing-free straight-edge spanning cycles that can be embedded over any specific set of $N$ points in the plane, improving upon the previous best upper bound $O(68.7^N)$. 
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[![Fig5][1]][1]


  [1]: https://i.sstatic.net/fA1EE.jpg