Irreducible Triangulations are Small

Details Irreducible Triangulations are Small Irreducible Triangulations are Small

2009-07-09

arxiv.org/abs/0907.1421v2

J. Combinatorial Theory Series B 100(5):446-455, 2010

Mathematics

Combinatorics

v2: Referees' comments incorporated

Scientific paper

10.1016/j.jctb.2010.01.004

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 $171g-72$.

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