Topological Ramsey theorem for complete bipartite graphs (Q1333333)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Topological Ramsey theorem for complete bipartite graphs |
scientific article; zbMATH DE number 638654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological Ramsey theorem for complete bipartite graphs |
scientific article; zbMATH DE number 638654 |
Statements
Topological Ramsey theorem for complete bipartite graphs (English)
0 references
13 September 1994
0 references
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.
0 references
Ramsey theorem
0 references
embedding
0 references
knot
0 references
link
0 references
spatial graph
0 references
complete bipartite graphs
0 references
complete multipartite graphs
0 references
complete graphs
0 references
