On the non-orientable genus of a 2-connected graph
type: Item
instance of: scholarly article
title: On the non-orientable genus of a 2-connected graph
zbMATH Open document ID: 0591.05026
DOI: 10.1016/0095-8956(87)90029-3
author: R. B. Richter
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: In earlier works, additivity theorems for the genus and Euler genus of unions of graphs at two points have been given. In this work, the analogous result for the non-orientable genus is given. If \(\Sigma\) is obtained from the sphere by the addition of \(k>0\) crosscaps, define \(\tilde\gamma(\Sigma)\) to be k. For a graph G, define \({\tilde \gamma}\)(G) to be the least element in the set \(\{\tilde \gamma(\Sigma)|\) G embeds in \(\Sigma\}\). Theorem: Let \(H_ 1\) and \(H_ 2\) be connected graphs such that \(H_ 1\cap H_ 2\) consists of the isolated vertices v and w. Then, for some \(\mu \in \{-1,0,1,2\}\), \(\tilde \gamma(H_ 1\cup H_ 2) = \tilde\gamma(H_ 1)+\tilde\gamma(H_ 2)+\mu\). A formula for \(\mu\) is given.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 3948296
zbMATH Keywords: graph embedding
zbMATH Keywords: genus of graphs
zbMATH Keywords: Euler genus
zbMATH Keywords: non-orientable genus
MaRDI profile type: Publication
full work available at URL: 0095-8956(87)90029-3
OpenAlex ID: W2094473531
cites work: The orientable genus is nonadditive
cites work: The nonorientable genus is additive
cites work: Additivity of the genus of a graph
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cites work: Permutation-Partition Pairs: A Combinatorial Generalization of Graph Embeddings
cites work: Blocks and the nonorientable genus of graphs
description: scientific article; zbMATH DE number 3948296