Surface triangulations with isometric boundary

✍ Scribed by Steve Fisk; Bojan Mohar

• Book ID: 103058492
• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 912 KB
• Volume: 134
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)e0059-d

✦ Synopsis

Let T be a triangulation of a bordered compact surface, and let C be a boundary component of T. Consider the metric on V(T) as determined by the l-skeleton of T. T is isometric with respect to C if for any two vertices of C their distance in Tis equal to the distance on C. Let n be the number of vertices on C, and assume that the number of vertices on all other boundary components of T is o(n). If T is an isometric triangulation of the disk with holes then 1 V(T)1 = Cl(n'). T is irreducible if the contraction of any interior edge results in a nonisometric triangulation or changes the homeomorphism type of the surface. It is shown that the number of combinatorially distinct irreducible isometric triangulations of a fixed surface with n vertices on the boundary is finite for each n.