4 citations · 13 across the 14 of their papers we have counts for
16 papers
Three thousand obstructions to knotless embedding
Thomas W Mattman, Andrei Pavelescu
We present a list of 3028 obstructions to knotless embedding. We survey recent work in this area including: 1) A bibliography of graphs proven to be intrinsically knotted without r…
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…
Complete Minors in Complements of Non-Separating Planar Graphs
Leonard Fowler, Gregory Li, Andrei Pavelescu
We prove that the complement of any non-separating planar graph of order contains a minor, and argue that the order is lowest possible with this property. To il…
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}…
Simple Graphs of Order 12 and Minimum Degree 6 Contain K_6 Minors
Ryan Odeneal, Andrei Pavelescu
We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
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.
Derangements in Cosets of Primitive Permutation Groups
Andrei Pavelescu
Motivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed point free elements…
Some Maximal Commutative Subrings of M_n(D)
Andrei Pavelescu
We answer a question of Weibel and show that maximal commutative subgrings of Artinian semisimple rings are direct products of local rings.