Yuanan Diao
The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers.
Fri, 12/18/2009 - 16:01 — SomNambulAuthors: Yuanan Diao, Claus Ernst, Attila Por, Uta Ziegler
Subjects: Geometric Topology
AbstractFor a knot or link K, let L(K) be the ropelength of K and Cr(K) be the
crossing number of K. In this paper, we show that there exists a constant a>0
such that L(K) is bounded above by a Cr(K) ln^5 (Cr(K)) for any knot K. This
result shows that the upper bound of the ropelength of any knot is almost
linear in terms of its minimum crossing number.Relative Tutte Polynomials for Colored Graphs and Virtual Knot Theory.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Yuanan Diao, Gabor Hetyei
Subjects: Combinatorics
AbstractWe introduce the concept of a relative Tutte polynomial of colored graphs. We
show that this relative Tutte polynomial can be computed in a way similar to
the classical spanning tree expansion used by Tutte in his original paper on
this subject. We then apply the relative Tutte polynomial to virtual knot
theory.Relative Tutte Polynomials for Colored Graphs and Virtual Knot Theory.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Yuanan Diao, Gabor Hetyei
Subjects: Combinatorics
AbstractWe introduce the concept of a relative Tutte polynomial of colored graphs. We
show that this relative Tutte polynomial can be computed in a way similar to
the classical spanning tree expansion used by Tutte in his original paper on
this subject. We then apply the relative Tutte polynomial to virtual knot
theory.
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