Les hypercartes planaires sont des arbres très bien étiquetés. (Planar hypermaps are well-labeled trees)
type: Item
instance of: scholarly article
title: Les hypercartes planaires sont des arbres très bien étiquetés. (Planar hypermaps are well-labeled trees)
zbMATH Open document ID: 0602.05023
DOI: 10.1016/0012-365X(86)90182-2
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Maps and hypermaps are defined combinatorially, in terms of permutations of a finite set, as in [\textit{R. Cori}, Astérisque 27, 1-169 (1975; Zbl 0313.05115)]. A bijection between rooted planar maps and rooted well- labelled trees (trees whose vertices are labelled with non-negative integers that differ by at most 1 on adjacent vertices) was established in [\textit{R. Cori} and \textit{B. Vauquelin}, Can. J. Math. 33, 1023-1042 (1981; Zbl 0415.05020)]. The paper under review presents a different bijection between rooted planar maps and rooted well-labelled trees, one which has the advantage of being extendable to a bijection between rooted planar hypermaps and rooted very well-labelled trees (well-labelled trees such that adjacent vertices have distinct labels). The latter bijection is a composition of the former with the reviewer's bijection between hypermaps and bipartite maps of the same genus [\textit{T. R. S. Walsh}, J. Comb. Theory, Ser. B 18, 155-163 (1975; Zbl 0302.05101)].
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 3970772
zbMATH Keywords: rooted planar maps
zbMATH Keywords: rooted well-labelled trees
zbMATH Keywords: bijection
author: Didier G. Arquès
reviewed by: Timothy R. S. Walsh
MaRDI profile type: Publication
cites work: Planar Maps are Well Labeled Trees
cites work: Hypermaps versus bipartite maps
description: scientific article; zbMATH DE number 3970772