9 citations · 43 across the 11 of their papers we have counts for
13 papers · 1 filter
Maximal knotless graphs
Lindsay Eakins, Thomas Fleming, Thomas W. Mattman
A graph is maximal knotless if it is edge maximal for the property of knotless embedding in . We show that such a graph has at least edges, and construct an infi…
Classifying Intrinsically Linked Tournaments by Score Sequence
Thomas Fleming, Joel Foisy
A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequenc…
Intrinsic linking and knotting in tournaments
Thomas Fleming, Joel Foisy
A directed graph is if every embedding of that graph contains a non-split link , where each component of is a consistently oriented cycle…
Intrinsically Knotted and 4-Linked Directed Graphs
Thomas Fleming, Joel Foisy
We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in eve…
Homotopy, Delta-equivalence and concordance for knots in the complement of a trivial link
Thomas Fleming, Tetsuo Shibuya, Tatsuya Tsukamoto +1
Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a lin…
Intrinsically Linked Graphs with Knotted Components
Thomas Fleming
We construct a graph G such that any embedding of G into R^{3} contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for a…