Exponential families of non-isomorphic triangulations of complete graphs
type: Item
instance of: scholarly article
title: Exponential families of non-isomorphic triangulations of complete graphs
zbMATH Open document ID: 1023.05041
author: C. Paul Bonnington
author: Michael John Grannell
author: T. S. Griggs
author: Jozef Širáň
published in: Journal of Combinatorial Theory. Series B
publication date: 2000-06-25T00:00:00Z
review text: It is shown that for \(n\equiv 7\) or \(19\pmod{36}\), there are at least \(2^{n^2/54- O(n)}\) non-isomorphic triangular embeddings of \(K_n\) in an orientable surface, all of which are face 2-colourable. When \(n\equiv 19\) or \(55\pmod{108}\) this estimate can be increased to \(2^{2n^2/81- O(n)}\). A similar estimate is established for non-orientable embeddings when \(n\equiv 1\) or \(7\pmod{18}\) (and an improved estimate in the cases when \(n\equiv 1\) or \(19\pmod{54}\)).
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1464307
zbMATH Keywords: Steiner triple system
zbMATH Keywords: non-isomorphic triangular embeddings
zbMATH Keywords: face 2-colourable
MaRDI profile type: Publication
full work available at URL: jctb.1999.1939
OpenAlex ID: W2034485257
cites work: Face 2-colourable triangular embeddings of complete graphs
cites work: Surface embeddings of Steiner triple systems
cites work: On the number of nonisomorphic orientable regular embeddings of complete graphs
cites work: Three nonisomorphic triangulations of an orientable surface with the same complete graph
cites work: Q4773723
cites work: Block designs and graph imbeddings
cites work: Nonisomorphic Steiner triple systems
cites work: Q5609151
DOI: 10.1006/JCTB.1999.1939
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description: scientific article; zbMATH DE number 1464307