An intrinsic nontriviality of graphs

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

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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

Volume 9, issue 1 (2009)

Ryo Nikkuni

Abstract