Volume 9, issue 1 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
An intrinsic nontriviality of graphs

Ryo Nikkuni

Algebraic & Geometric Topology 9 (2009) 351–364
Abstract

We say that a graph is intrinsically nontrivial if every spatial embedding of the graph contains a nontrivial spatial subgraph. We prove that an intrinsically nontrivial graph is intrinsically linked, namely every spatial embedding of the graph contains a nonsplittable 2–component link. We also show that there exists a graph such that every spatial embedding of the graph contains either a nonsplittable 3–component link or an irreducible spatial handcuff graph whose constituent 2–component link is split.

Dedicated to Professor Akio Kawauchi on his 60th birthday

Keywords
spatial graph, intrinsically linked, spatial handcuff graph
Mathematical Subject Classification 2000
Primary: 57M15
Secondary: 57M25
References
Publication
Received: 30 July 2008
Revised: 29 January 2009
Accepted: 31 January 2009
Published: 23 February 2009
Authors
Ryo Nikkuni
Institute of Human and Social Sciences
Faculty of Teacher Education
Kanazawa University
Kakuma-machi, Kanazawa, Ishikawa, 920-1192
Japan
http://www.ed.kanazawa-u.ac.jp/~nick/index-e.html