Limit points for average genus. II: 2-connected non-simplicial graphs
type: Item
instance of: scholarly article
title: Limit points for average genus. II: 2-connected non-simplicial graphs
zbMATH Open document ID: 0776.05036
DOI: 10.1016/0095-8956(92)90011-L
author: Jonathan L. Gross
author: Jianer Chen
published in: Journal of Combinatorial Theory. Series B
publication date: 1993-03-10T00:00:00Z
review text: The average genus of a graph \(G\) is the average value of the genus of the imbedding surface, taken over all orientable embeddings of \(G\). Given a collection of graphs, the authors consider the set of values of the average genus of these graphs; specifically, does this set have a limit point? The idea behind the question is how well does the average value serve to distinguish between graphs in the collection. In Part I of this paper [ibid., Ser. B 55, No. 1, 83-103 (1992; Zbl 0709.05017)] the authors proved that there are no limit points for the average genus of 2- connected simplicial (simple) graph or for the average genus of 3- connected graphs. In this paper the authors give a systematic method for constructing sequences of 2-connected nonsimplicial graphs whose average genus converges to a limit point. Their construction involves a variation on necklaces, which have been used before in this context. They also prove that their method is in a sense unique.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 130564
zbMATH Keywords: average genus
zbMATH Keywords: embeddings
zbMATH Keywords: necklaces
reviewed by: Dan S. Archdeacon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 130564