A linklessly embeddable graph is a graph having the property that there exists an embedding in three dimensions that does not contain a nontrivial
link. A graph is linklessly embeddable iff
it does not contain one of the seven Petersen
family graphs as a forbidden minor (Robertson
et al. 1993).
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 217-221, 1994.Naimi, R.; Pavelescu,
A.; and Pavelescu, E. "New Bounds of Maximal Linkless Graphs." 20 Sep 2020.
https://arxiv.org/abs/2007.10522.Odeneal,
Y.; Naimi, R.; Pavelescu, A.; and Pavelescu, E. "The Complement Problem for
Linklessly Embeddable Graphs." J. Knot Theory and Its Ramifications 2250075,
1-10, 2022.Robertson, N.; Seymour, P. D.; and Thomas, R. "Linkless
Embeddings of Graphs in 3-Space." Bull. Amer. Math. Soc.28, 84-89,
1993.
among their forbidden minors (Robertson et
al. 1993).
