Kuratowski-type theorems for average genus
type: Item
instance of: scholarly article
title: Kuratowski-type theorems for average genus
zbMATH Open document ID: 0776.05037
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 \(G\). In general one expects this number to be large. Calculations reveal it to be close to the maximum genus. In this paper the authors give a list of all cut-edge-free graphs whose average genus is less than or equal to 1. This list consists of a finite number of small graphs, which are given in the paper, and an infinite class of graphs called necklaces (a necklace is a slight variation on a cactus). The authors also give a Kuratowski-type theorem characterizing graphs of maximum genus 1.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 130576
zbMATH Keywords: average genus
zbMATH Keywords: embeddings
zbMATH Keywords: maximum genus
zbMATH Keywords: necklace
zbMATH Keywords: Kuratowski-type theorem
reviewed by: Dan S. Archdeacon
MaRDI profile type: Publication
OpenAlex ID: W2071534778
DOI: 10.1006/JCTB.1993.1009
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description: scientific article; zbMATH DE number 130576