English

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.

Keywords

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

R2 v1 2026-06-21T10:34:51.784Z