Irreducible Triangulations are Small
classification
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irreduciblesurfacetriangulationanotherbestboundcontractionedge
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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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