37 citations · 136 across the 23 of their papers we have counts for
4 papers · 1 filter
Counting Plane Graphs: Perfect Matchings, Spanning Cycles, and Kasteleyn's Technique
Micha Sharir, Adam Sheffer, Emo Welzl
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…
Bounds on the maximum multiplicity of some common geometric graphs
Adrian Dumitrescu, André Schulz, Adam Sheffer +1
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in general…
Counting Plane Graphs: Flippability and its Applications
Michael Hoffmann, Micha Sharir, Adam Sheffer +2
We generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set S of points in the plane to so-called \emph{pseudo-simultaneously flippable ed…
Counting Triangulations of Planar Point Sets
Micha Sharir, Adam Sheffer
We study the maximal number of triangulations that a planar set of points can have, and show that it is at most . This new bound is achieved by a careful optimization of…