12 citations · 51 across the 19 of their papers we have counts for
22 papers
New minor minimal non-apex graphs
Andrei Pavelescu, Elena Pavelescu, Madeline Potter
A graph is apex if it becomes planar after the deletion of one vertex. The family of apex graphs is closed under taking minors, so it is characterized by a finite set of forbidden…
Intrinsically knotted graphs and connected domination
Gregory Li, Andrei Pavelescu, Elena Pavelescu
We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination…
The total chord length of maximal outerplanar graphs
Haley Broadus, Elena Pavelescu
We consider embeddings of maximal outerplanar graphs whose vertices all lie on a cycle bounding a face. Each edge of the graph that is not in , a chord,…
Connected Domination in Plane Triangulations
Felicity Bryant, Elena Pavelescu
A set of vertices of a graph such that each vertex of is either in the set or is adjacent to a vertex in the set is called a dominating set of . If additionally, the set…
The Extremal Function for Apex Graphs
Elena Pavelescu
McCarty and Thomas conjectured that a linklessly embeddable graph with vertices and triangles has at most edges. Thomas and Yoo proved this to be…
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…
An infinite family of linklessly embeddable Tutte-4-connected graphs
Andrei Pavelescu, Elena Pavelescu
For each , we provide an example of a linklessly embeddable, Tutte-4-connected graph of order .
Constructions stemming from non-separating planar graphs and their Colin de Verdière invariant
Andrei Pavelescu, Elena Pavelescu
A planar graph is said to be non-separating if there exists an embedding of in such that for any cycle , all vertices of $G\setminus \m…
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}…
The complement of a nIL graph with thirteen vertices is IL
Andrei Pavelescu, Elena Pavelescu
We show that for any simple non-oriented graph G with at least thirteen vertices either G or its complement is intrinsically linked.
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.
Hadwiger numbers of self-complementary graphs
Andrei Pavelescu, Elena Pavelescu
The Hadwiger number of a graph , denoted by , is the order of the largest complete minor of . A graph is said to be self-complementary if it is isomorphic to its comple…
Complete Minors of Self-Complementary Graphs
Andrei Pavelescu, Elena Pavelescu
We show that any self-complementary graph with vertices contains a minor. We derive topological properties of self-complementary graphs.
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…
Deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph
Ramin Naimi, Elena Pavelescu, Hannah Schwartz
We show that deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph.
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…