21 citations · 91 across the 23 of their papers we have counts for
26 papers · 1 filter
Splittings of Tangles and Spatial Graphs
Erica Flapan, Hugh Howards
Menasco proved the surprising result that if is a reduced, alternating, connected projection of a link and is prime then is prime. This result has been generalized…
Weakly linked embeddings of pairs of complete graphs in
James Di, Erica Flapan, Spencer Johnson +2
Let and be disjoint embeddings of complete graphs and in such that some cycle in links a cycle in with non-zero linking number. We say th…
Topological Symmetry Groups of the Heawood Graph
Emille Davie Lawrence, Erica Flapan, Robin T. Wilson
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in .
Stick number of non-paneled knotless spatial graphs
Erica Flapan, Kenji Kozai, Ryo Nikkuni
We show that the minimum number of sticks required to construct a non-paneled knotless embedding of is 9 and of is 12 or 13. We use our results about to show that…
Symmetries of Spatial Graphs in -manifolds
Erica Flapan, Song Yu
We consider when automorphisms of a graph can be induced by homeomorphisms of embeddings of the graph in a -manifold. In particular, we prove that every automorphism of a graph…
Recent Developments in Spatial Graph Theory
Erica Flapan, Thomas Mattman, Blake Mellor +2
This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results abo…
Ravels arising from Montesinos Tangles
Erica Flapan, Allison N. Miller
A ravel is a spatial graph which is non-planar but contains no non-trivial knots or links. We characterize when a Montesinos tangle can become a ravel as the result of vertex closu…
Linking number and writhe in random linear embeddings of graphs
Erica Flapan, Kenji Kozai
In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Ou…
Intrinsic Chirality of Graphs in 3-manifolds
Erica Flapan, Hugh Howards
The main result of this paper is that for every closed, connected, orientable, irreducible 3-manifold , there is an integer such that any abstract graph with no automorph…
Knotted and linked products of recombination on substrates
Erica Flapan, Jeremy Grevet, Qi Li +2
We develop a topological model of site-specific recombination that applies to substrates which are the connected sum of two torus links of the form . Then we use ou…
Reduced Wu and Generalized Simon Invariants for Spatial Graphs
Erica Flapan, Will Fletcher, Ryo Nikkuni
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain l…
Topological Symmetry Groups of Möbius Ladders
Erica Flapan, Emille Davie Lawrence
We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in .
Intrinsic Chirality of Multipartite Graphs
Erica Flapan, Will Fletcher
We classify which complete multipartite graphs are intrinsically chiral.
Topological Symmetry Groups for Small Complete Graphs
Dwayne Chambers, Erica Flapan
For each , we characterize all the groups which can occur as either the orientation preserving topological symmetry group or the topological symmetry group of some embeddi…
The Y-triangle move does not preserve Intrinsic Knottedness
Erica Flapan, Ramin Naimi
We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted gr…
Symmetries of embedded complete bipartite graphs
Erica Flapan, Nicole Lehle, Blake Mellor +2
We characterize which automorphisms of an arbitrary complete bipartite graph can be induced by a homeomorphism of some embedding of the graph in .
Classification of topological symmetry groups of
Erica Flapan, Blake Mellor, Ramin Naimi +1
In this paper we complete the classification of topological symmetry groups for complete graphs by characterizing which can have a cyclic group, a dihedral group, or a…
Topological Symmetry Groups of Graphs in 3-Manifolds
Erica Flapan, Harry Tamvakis
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedd…
Spatial Graphs with Local Knots
Erica Flapan, Blake Mellor, Ramin Naimi
It is shown that for any locally knotted edge of a 3-connected graph in , there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setw…
Complete graphs whose topological symmetry groups are polyhedral
Erica Flapan, Blake Mellor, Ramin Naimi
We determine for which , the complete graph has an embedding in whose topological symmetry group is isomorphic to one of the polyhedral groups: , , or $S_4…
Topological Symmetry Groups of K_{4r+3}
Dwayne Chambers, Erica Flapan, John D. O'Brien
We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the to…
Every graph has an embedding in containing no non-hyperbolic knot
Erica Flapan, Hugh Howards
In contrast with knots, whose properties depend only on their extrinsic topology in , there is a rich interplay between the intrinsic structure of a graph and the extrinsic to…
A Topological Characterization Of Knots and Links Arising From Site-Specific Recombination
Dorothy Buck, Erica Flapan
We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or l…
Intrinsic linking and knotting are arbitrarily complex
Erica Flapan, Blake Mellor, Ramin Naimi
We show that, given any and , every embedding of any sufficiently large complete graph in contains an oriented link with components , ..., such tha…