Ramin Naimi

INTRINSICALLY n-LINKED GRAPHS

For every natural number n, we exhibit a graph with the property that every embedding of it in ℝ3 contains a non-split n-component link. Furthermore, we prove that our graph is minor minimal in the sense that every minor of it has an embedding in ℝ3 that contains no non-split n-component link.

Intrinsically Triple Linked Complete Graphs

Abstract We prove that every embedding of K 10 in R 3 contains a non-split link of three components. We also exhibit an embedding of K 9 with no such link of three components.

Many, many more intrinsically knotted graphs

We list more than 200 new examples of minor minimal intrinsically knotted graphs and describe many more that are intrinsically knotted and likely minor minimal.

Topological symmetry groups of graphs embedded in the 3-sphere

The topological symmetry group of a graph embedded in the 3-sphere is the group consisting of those automorphisms of the graph which are induced by some homeomorphism of the ambient space. We prove strong restrictions on the groups that can occur as the topo- logical symmetry group of some embedded graph. In addition, we characterize the orientation preserving topological symmetry groups of embedded 3-connected graphs in the 3-sphere.

Topological Symmetry Groups of Complete Graphs in the 3-Sphere

The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induced by an orientation preserving homeomorphism of the ambient space. We characterize all possible orientation preserving topological symmetry groups of embeddings of complete graphs in the 3-sphere.

Complete Graphs whose Topological Symmetry Groups are Polyhedral

We determine for which

Linear embeddings of K9 are triple linked

m

Induced subgraphs of Johnson graphs

, the complete graph

On the number of links in a linearly embedded K3,3,1

K_m

An Algorithm for Detecting Intrinsically Knotted Graphs

has an embedding in