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2009 An intrinsic nontriviality of graphs
Ryo Nikkuni
Algebr. Geom. Topol. 9(1): 351-364 (2009). DOI: 10.2140/agt.2009.9.351

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.

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Ryo Nikkuni. "An intrinsic nontriviality of graphs." Algebr. Geom. Topol. 9 (1) 351 - 364, 2009. https://doi.org/10.2140/agt.2009.9.351

Information

Received: 30 July 2008; Revised: 29 January 2009; Accepted: 31 January 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1170.57003
MathSciNet: MR2482082
Digital Object Identifier: 10.2140/agt.2009.9.351

Subjects:
Primary: 57M15
Secondary: 57M25

Rights: Copyright © 2009 Mathematical Sciences Publishers

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