12 citations · 51 across the 19 of their papers we have counts for
11 papers · 1 filter
Intrinsically knotted graphs with linklessly embeddable simple minors
Thomas W. Mattman, Ramin Naimi, Andrei Pavelescu +1
It has been an open question whether the deletion or contraction of an edge in an intrinsically knotted graph always yields an intrinsically linked graph. We present a new intrinsi…
The Complement Problem for Linklessly Embeddable Graphs
Ramin Naimi, Ryan Odeneal, Andrei Pavelescu +1
We find all maximal linklessly embeddable graphs of order up to 11, and verify that for every graph of order 11 either or its complement is intrinsically linked. We gi…
New bounds on maximal linkless graphs
Ramin Naimi, Andrei Pavelescu, Elena Pavelescu
We construct a family of maximal linklessly embeddable graphs on vertices and edges for all , and another family on vertices and $m< \frac{25n}{12}-\frac{1}…
Escher squares and lattice links
Ramin Naimi, Andrei Pavelescu, Elena Pavelescu
We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.
The total Thurston-Bennequin number of complete and complete bipartite Legendrian graphs
Danielle O'Donnol, Elena Pavelescu
We study the Thurston-Bennequin number of complete and complete bipartite Legendrian graphs. We define a new invariant called the total Thurston-Bennequin number of the graph. We s…
Legendrian theta-graphs
Danielle O'Donnol, Elena Pavelescu
In this article we give necessary and sufficient conditions for two triples of integers to be realized as the Thurston-Bennequin number and the rotation number of a Legendrian thet…
On the number of links in a linearly embedded
Ramin Naimi, Elena Pavelescu
We show there exists a linear embedding of with n nontrivial 2-component links if and only if n = 1, 2, 3, 4, or 5.
Linear embeddings of are triple linked
Ramin Naimi, Elena Pavelescu
We use the theory of oriented matroids to show that any linear embedding of , the complete graph on nine vertices, contains a non-split link with three components.
On Legendrian Graphs
Danielle O'Donnol, Elena Pavelescu
We investigate Legendrian graphs in . We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph…
Braiding Knots in Contact 3-Manifolds
Elena Pavelescu
We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures…
The Self-Linking Number in Annulus and Pants Open Book Decompositions
Keiko Kawamuro, Elena Pavelescu
We find a self-linking number formula for a given null-homologous transverse link in a contact manifold that is compatible with either an annulus or a pair of pants open book decom…