On the Euler genus of a 2-connected graph
type: Item
instance of: scholarly article
title: On the Euler genus of a 2-connected graph
zbMATH Open document ID: 0591.05025
DOI: 10.1016/0095-8956(87)90030-X
author: R. B. Richter
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: The Euler genus of the surface \(\Sigma\) obtained from the sphere by the addition of k crosscaps and h handles in \(\epsilon (\Sigma)=k+2h\). For a graph G, the Euler genus \(\epsilon(G)\) of G is the smallest Euler genus among all surfaces in which G embeds. The following additivity theorem is proved: Suppose \(G=H\cup K\), where H and K have exactly the vertices v and w in common. Then \(\epsilon (G)=\min \{\epsilon (H+vw)+\epsilon (K+vw),\quad \epsilon (H)+\epsilon (K)+2\}.\)
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 3948295
zbMATH Keywords: graph embedding
zbMATH Keywords: genus of graphs
zbMATH Keywords: Euler genus
zbMATH Keywords: surface
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3948295