Enumeration of Eulerian and unicursal planar maps

DOI10.1016/j.disc.2003.09.015zbMath1051.05049OpenAlexW2164323648MaRDI QIDQ1827745

Valery A. Liskovets, Timothy R. S. Walsh

Publication date: 6 August 2004

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2003.09.015

zbMATH Keywords

bipartiteembeddingLagrange inversionrooted planar mapsum-free formulaunrooted Eulerian map

Mathematics Subject Classification ID

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

Related Items (12)

A family of Bell transformations ⋮ A character approach to directed genus distribution of graphs: the bipartite single-black-vertex case ⋮ Counting unrooted maps on the plane ⋮ On the enumeration of hypermaps which are self-equivalent with respect to reversing the colors of vertices ⋮ Corrigendum to: ``Enumeration of Eulerian and unicursal planar maps ⋮ Counting rooted 4-regular unicursal planar maps ⋮ Counting rooted unicursal planar maps ⋮ Enumeration of unrooted hypermaps of a given genus ⋮ Counting unrooted loopless planar maps ⋮ Efficient enumeration of sensed planar maps ⋮ Enumeration of unrooted hypermaps ⋮ Enumeration of rooted 3-connected bipartite planar maps

Cites Work

• Unnamed Item
• Curvature matrix models for dynamical triangulations and the Itzykson-Di Francesco formula
• Census of planar maps: From the one-matrix model solution to a combinatorial proof
• Matrix integrals and map enumeration: an accessible introduction
• A survey of the asymptotic behaviour of maps
• Une nouvelle demonstration combinatoire des formules d'inversion de Lagrange
• Counting rooted maps by genus. III: Nonseparable maps
• Hypermaps versus bipartite maps
• A pattern of asymptotic vertex valency distributions in planar maps
• Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
• Enumeration of planar constellations
• Character expansion methods for matrix models of dually weighted graphs
• A Census of Slicings
• Some Asymptotical Estimates for Planar Eulerian Maps
• On the Average Number of Trees in Certain Maps
• A Census of Planar Maps
• Enumeration of simple bipartite maps on the sphere and the projective plane

This page was built for publication: Enumeration of Eulerian and unicursal planar maps