Irreducible Triangulations are Small

Gwenaël Joret, David R. Wood

Published 2009-07-09, updated 2010-02-19Version 2

A triangulation of a surface is \emph{irreducible} if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus $g\geq1$ has at most $13g-4$ vertices. The best previous bound was $171g-72$.