Add to ORKGApplying Jaco’s Handle Addition Lemma, we give a condition for a 3-manifold to have an incompressible boundary. As an application, we show that the boundary of the exterior of a minimally knotted planar graph is incompressible.
AbstractWe prove that the complements of all knots and links in S3 which have a 2n-plat projection w...
AbstractA spatial embedding of a graph G is an embedding of G into the 3-dimensional Euclidean space...
Two fundamental objects in knot theory are the minimal genus surface and the least area surface boun...
AbstractWe address the following unknotting conjecture for graphs. If G is a planar graph embedded i...
In the field of topology, a graph is a set of vertices with certain vertices connected to each other...
Abstract. We show that all nontrivial embeddings of planar graphs on the torus contain a nontrivial ...
Abstract. We show that if there exists an essential accidental surface in the knot exterior, then a ...
AbstractIn this paper, we study spatial-graph isotopy for trivalent graphs, and give a connection be...
Let G be a finite graph. We give a label to each of vertices and edges of G. An embedding of G into ...
PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.li...
Abstract. Given a compact orientable 3–manifold M whose boundary is a hyperbolic surface and a simpl...
Our research focused on two questions in graph and knot theory. Our first question addressed the com...
We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is int...
AbstractGiven a graph in 3-space, in general knotted, can one construct a surface containing the gra...
If H is a spatial handlebody, i.e. a handlebody embedded in the 3-sphere, a spine of H is a graph Γ...
AbstractWe prove that the complements of all knots and links in S3 which have a 2n-plat projection w...
AbstractA spatial embedding of a graph G is an embedding of G into the 3-dimensional Euclidean space...
Two fundamental objects in knot theory are the minimal genus surface and the least area surface boun...
AbstractWe address the following unknotting conjecture for graphs. If G is a planar graph embedded i...
In the field of topology, a graph is a set of vertices with certain vertices connected to each other...
Abstract. We show that all nontrivial embeddings of planar graphs on the torus contain a nontrivial ...
Abstract. We show that if there exists an essential accidental surface in the knot exterior, then a ...
AbstractIn this paper, we study spatial-graph isotopy for trivalent graphs, and give a connection be...
Let G be a finite graph. We give a label to each of vertices and edges of G. An embedding of G into ...
PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.li...
Abstract. Given a compact orientable 3–manifold M whose boundary is a hyperbolic surface and a simpl...
Our research focused on two questions in graph and knot theory. Our first question addressed the com...
We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is int...
AbstractGiven a graph in 3-space, in general knotted, can one construct a surface containing the gra...
If H is a spatial handlebody, i.e. a handlebody embedded in the 3-sphere, a spine of H is a graph Γ...
AbstractWe prove that the complements of all knots and links in S3 which have a 2n-plat projection w...
AbstractA spatial embedding of a graph G is an embedding of G into the 3-dimensional Euclidean space...
Two fundamental objects in knot theory are the minimal genus surface and the least area surface boun...