Ramsey-type theorems for spatial graphs and good drawings
type: Item
instance of: scholarly article
title: Ramsey-type theorems for spatial graphs and good drawings
zbMATH Open document ID: 0913.05040
author: Seiya Negami
published in: Journal of Combinatorial Theory. Series B
publication date: 1998-05-24T00:00:00Z
review text: A drawing of a graph \(G\) in the plane is said to be good if the following conditions are satisfied: (1) points representing the vertices are all distinct; (2) each edge is represented by a simple arc; (3) any two adjacent edges intersect only at a common end; and (4) any two non-adjacent edges cross in at most one point. A spatial embedding of \(G\) is good if, after applying a suitable ambient isotopy to \(G\), its canonical projection onto the \(xy\)-plane is a good drawing of \(G\). The author has proven the following Ramsey-type theorem: Given a spatial graph \(H\) there exists a pair of natural numbers \((N,M)\) such that any good spatial embedding of \(K_{N,M}\) contains a subgraph which is ambient isotopic to a subdivision of \(H\). This result generalizes earlier results of the author where the role of good drawings was played by rectilinear drawings.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 1154559
zbMATH Keywords: spatial embedding
zbMATH Keywords: good drawing
zbMATH Keywords: Ramsey-type theorem
reviewed by: Martin Škoviera
MaRDI profile type: Publication
full work available at URL: jctb.1997.1783
OpenAlex ID: W2055026392
cites work: Knots and links in spatial graphs
cites work: Q3903002
cites work: On Invariants of Graphs with Applications to Knot Theory
cites work: Topological Ramsey theorem for complete bipartite graphs
cites work: Ramsey Theorems for Knots, Links and Spatial Graphs
DOI: 10.1006/JCTB.1997.1783
description: scientific article; zbMATH DE number 1154559