Topological Ramsey theorem for complete bipartite graphs
type: Item
instance of: scholarly article
title: Topological Ramsey theorem for complete bipartite graphs
zbMATH Open document ID: 0802.05056
author: Miki Shimabara Miyauchi
published in: Journal of Combinatorial Theory. Series B
publication date: 1994-09-13T00:00:00Z
review text: An embedding of a graph into a space is linear if each edge is a straight line segment. In 1991, \textit{S. Negami} [Trans. Am. Math. Soc. 324, No. 2, 527-541 (1991; Zbl 0721.57004)] showed that for any given knot, link, or spatial graph there is a sufficiently large complete graph \(K_ n\) such that every linear embedding of \(K_ n\) into a space always contains that knot, link, or spatial graph. This paper generalizes this result to cover complete bipartite graphs. The results for complete multipartite graphs and for complete graphs are obtained as corollaries.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M15
zbMATH DE Number: 638654
zbMATH Keywords: Ramsey theorem
zbMATH Keywords: embedding
zbMATH Keywords: knot
zbMATH Keywords: link
zbMATH Keywords: spatial graph
zbMATH Keywords: complete bipartite graphs
zbMATH Keywords: complete multipartite graphs
zbMATH Keywords: complete graphs
MaRDI profile type: Publication
full work available at URL: jctb.1994.1061
OpenAlex ID: W1965252513
DOI: 10.1006/JCTB.1994.1061
description: scientific article; zbMATH DE number 638654