Allison Henrich
Irredicibly Odd Graphs.
Fri, 08/20/2010 - 15:01 — SomNambulAuthors: Allison Henrich, Tomas Boothby
Subjects: Combinatorics
AbstractAn irreducibly odd graph is a graph such that each vertex has odd degree and
for every pair of vertices, a third vertex in the graph is adjacent to exactly
one of the pair. This family of graphs was introduced recently by Manturov in
relation to free knots. In this paper, we show that every graph is the induced
subgraph of an irreducibly odd graph. Furthermore, we prove that irreducibly
odd graphs must contain a particular minor called the triskelion.An Upper Bound on the Number of Reidemeister Moves Required to Unknot an Unknot.
Wed, 06/23/2010 - 15:01 — SomNambulAuthors: Allison Henrich, Louis H. Kauffman
Subjects: Geometric Topology
AbstractIn 1998, Hass and Lagarias found an upper bound for the number of
Reidemeister moves needed to unknot an unknot. This number is exponential in
the crossing number of a diagram. Using results from Dynnikov's 2004 paper
regarding arc-presentations of knots, we propose a significantly smaller bound.Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Allison Henrich, Noel MacNaughton, Sneha Narayan, Oliver Pechenik, Jennifer Townsend
Subjects: Geometric Topology
AbstractA pseudodiagram is a diagram of a knot with some crossing information
missing. We review and expand the theory of pseudodiagrams introduced by R.
Hanaki. We then extend this theory to the realm of virtual knots, a
generalization of knots. In particular, we investigate how much crossing
information must be known to conclude that a diagram is a diagram of the unknot
(the trivializing number). We provide a table of trivializing numbers for knots
with no more than 10 crossings, as well as an algorithm to calculate an upper
bound on the trivializing number of any knot.- Read more
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