Tight and untight triangulations of surfaces by complete graphs
type: Item
instance of: scholarly article
title: Tight and untight triangulations of surfaces by complete graphs
zbMATH Open document ID: 0832.05035
author: Jorge L. Arocha
author: Javier Bracho
author: V. Neumann-Lara
published in: Journal of Combinatorial Theory. Series B
publication date: 1995-07-02T00:00:00Z
review text: Embeddings of the complete graph \(K_n\) into surfaces is a classic topic in graph theory. This paper studies triangular embeddings of \(K_n\) into surfaces through the notion of tightness which is a natural combinatorial generalization of connectedness for graphs. The author defines a new operation among complete triangular surfaces, the coupling construction, which couples the combinatorial information of two complete triangulated surfaces with boundary of order \(n\) to produce a complete triangulated closed surface of order \(2n\) and hence yields many triangular embeddings of complete graphs into nonorientable surfaces. Applying the coupling construction, the author proves the existence of untight complete triangular embeddings and broadens the known archive of tight ones. In particular, it is shown that there exist two nonisomorphic triangular embeddings of \(K_{30}\), one tight and the other untight, in the same closed surface.
reviewed by: Hong Shen
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 767690
zbMATH Keywords: complete graph
zbMATH Keywords: surfaces
zbMATH Keywords: tightness
zbMATH Keywords: connectedness
zbMATH Keywords: complete triangular surfaces
zbMATH Keywords: coupling construction
zbMATH Keywords: triangular embeddings
zbMATH Keywords: closed surface
MaRDI profile type: Publication
full work available at URL: jctb.1995.1015
OpenAlex ID: W1978553161
DOI: 10.1006/JCTB.1995.1015
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description: scientific article; zbMATH DE number 767690