An intrinsic non-triviality of graphs
Geometric Topology
2016-01-20 v3
Abstract
We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exists a graph such that every spatial embedding of the graph contains either a non-splittable 3-component link or an irreducible spatial handcuff graph whose constituent 2-component link is split.
Cite
@article{arxiv.0804.4229,
title = {An intrinsic non-triviality of graphs},
author = {Ryo Nikkuni},
journal= {arXiv preprint arXiv:0804.4229},
year = {2016}
}
Comments
11 pages, 13 figures