12 citations · 51 across the 19 of their papers we have counts for
11 papers · 1 filter
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…
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…
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.
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.
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.