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Minimal ordered triangulations of surfaces
Author(s) -
Magajna Zlatan,
Mohar Bojan,
Pisanski Tomaž
Publication year - 1986
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190100405
Subject(s) - combinatorics , mathematics , bipartite graph , quadrilateral , triangulation , partially ordered set , embedding , euler characteristic , surface (topology) , simplicial complex , graph , discrete mathematics , geometry , computer science , physics , finite element method , artificial intelligence , thermodynamics
A finite simplicial complex is orderable if its simplices are the chains of a poset. For each closed surface an orderable triangulation is given that is minimal with respect to the number of vertices. The construction of minimal ordered triangulations implies that for each surface S the minimal number of vertices of a bipartite graph, which has a quadrilateral embedding into S , is equal to b(S) = ⌈4 + (16 – 8χ) 1/2 ⌉, where χ is the Euler characteristic of S .