Counting triangulations and pseudo-triangulations of wheels.
Dana Randall, Günter Rote, Francisco Santos, Jack Scott Snoeyink · 2001
Motivated by several open questions on triangulations and pseudotriangulations we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n points in wheel configurWWM#E3 that is, with n - 1in convex position. Although the number of triangulations and pseudotriangulations var depending on the placement of the inter]W point,their differ])M is always the (n - 2)nd Catalan number We also pr ve an inequality #PT # 3 i #Tfor the number of minimum pseudo-tr[W33MrMrM andtr# angulations of any point configur#3E] with i interior points.