Irreducible triangulations are small
Copyright policy )Irreducible triangulations are small
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 $171g-72$.
v2: Referees' comments incorporated
- Université Libre de Bruxelles Belgium
- University of Melbourne Australia
Topological graph theory, Extremal problems in graph theory, Pure Mathematics, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, topological graph theory, Computational Theory and Mathematics, Informatique mathématique, Irreducible triangulations, FOS: Mathematics, 05C10, 05C35, irreducible triangulations, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO)
Topological graph theory, Extremal problems in graph theory, Pure Mathematics, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, topological graph theory, Computational Theory and Mathematics, Informatique mathématique, Irreducible triangulations, FOS: Mathematics, 05C10, 05C35, irreducible triangulations, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO)
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