On a graph property generalizing planarity and flatness

H. Holst, van der, R.A. Pendavingh

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

We introduce a topological graph parameter s(G), defined for any graph G. This parameter characterizes subgraphs of paths, outerplanar graphs, planar graphs, and graphs that have a flat embedding as those graphs G with s(G)=1,2,3, and 4, respectively. Among several other theorems, we show that if H is a minor of G, then s(H)=s(G), that s(K n )=n-1, and that if H is the suspension of G, then s(H)=s(G)+1. Furthermore, we show that µ(G)=s(G) + 2 for each graph G. Here µ(G) is the graph parameter introduced by Colin de Verdière in [2].
Original languageEnglish
Pages (from-to)337-361
JournalCombinatorica
Volume29
Issue number3
DOIs
Publication statusPublished - 2009

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