2001/10/02 by Roland Bacher, Bacher, Roland, Alina Vdovina +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.CO #math.GR
paper · pdf · doi:10.48550/arxiv.math/0110025
15 pages, 2 figures
arxiv created 2001/10/02 · openalex publication_date 2001/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A \em 1-vertex triangulation of an oriented compact surface S of genus g is an embedded graph T⊂ S with a unique vertex such that all connected components of S∖ T are triangles (adjacent to exactly 3 edges of T). This paper gives formulas enumerating such triangulations (up to equivalence) on an oriented surface of given genus. \em Une triangulation à un sommet d'une surface orientée compacte S de genre g est un graphe T⊂ S qui a un unique sommet et dont toutes les faces (composantes connexes de S∖ T) sont des triangles (incidentes à trois arêtes de T). Cet article donne des formules permettant d'énumérer ces triangulations.