On intrinsically knotted or completely 3-linked graphs

2010/06/30 by Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics #Complement graph #Computational Geometry and Mesh Generation #Computer science #Discrete mathematics #Embedding #Geometric and Algebraic Topology #Graph #Knot (papermaking) #Line graph #Mathematics #Voltage graph #math.GT #msc:57M15 #msc:57M25

paper · pdf · doi:10.2140/pjm.2011.252.407

published as Pacific J. Math. 252 (2011), 407--425 · 17 pages, 9 figures

arxiv created 2011/01/21 · openalex publication_date 2011/10/29 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of \triangle Y-exchanges and Y \triangle-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

Citations

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