The asymptotic number of rooted maps on a surface. II: Enumeration by vertices and faces

DOI10.1016/0097-3165(93)90063-EzbMath0777.05065MaRDI QIDQ1801793

L. Bruce Richmond, Edward A. Bender, E. Rodney Canfield

Publication date: 17 August 1993

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

zbMATH Keywords

generating functionsasymptotic enumerationrooted maps

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10) Asymptotic enumeration (05A16)

Related Items (23)

Enumeration of cubic multigraphs on orientable surfaces ⋮ Blossoming bijection for bipartite pointed maps and parametric rationality of general maps of any surface ⋮ Feynman diagrams, ribbon graphs, and topological recursion of Eynard-Orantin ⋮ The mesoscopic geometry of sparse random maps ⋮ Counting 2-connected 4-regular maps on the projective plane ⋮ Blossoming bijection for higher-genus maps ⋮ The two-point function of bicolored planar maps ⋮ Cubic graphs and related triangulations on orientable surfaces ⋮ Asymptotic enumeration and limit laws for graphs of fixed genus ⋮ On the Diameter of Random Planar Graphs ⋮ Random graphs on surfaces ⋮ 4-edge-connected 4-regular maps on the projective plane ⋮ Énumération des cartes pointées sue la bouteille de Klein ⋮ Enumeration of \(N\)-rooted maps using quantum field theory ⋮ Submaps of maps. I: General 0-1 laws ⋮ Enumerating near-4-regular maps on the sphere and the torus ⋮ A bijection for essentially 3-connected toroidal maps ⋮ Counting rooted maps on an orientable surface of any genus by a function of the numbers of vertices and faces ⋮ Counting rooted maps on a surface ⋮ Le schéma de carte et ses applications ⋮ 4-regular maps on the Klein bottle ⋮ The number of loopless \(4\)-regular maps on the projective plane ⋮ Simple recurrence formulas to count maps on orientable surfaces

Cites Work

• The asymptotic enumeration of rooted convex polyhedra
• The asymptotic number of rooted maps on a surface
• Relations fonctionnelles et dénombrement des cartes pointées sur le tore. (Functional relations and the enumeration of rooted genus one maps)
• Random triangulations of the plane
• The number of rooted maps on an orientable surface
• Central and local limit theorems applied to asymptotic enumeration. II: Multivariate generating functions
• Almost all Convex Polyhedra are Asymmetric
• The Number of Three-Dimensional Convex Polyhedra
• Asymptotic Methods in Enumeration
• The Enumeration of Maps on the Torus and the Projective Plane
• On the enumeration of planar maps

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