Related papers: Identification of 2-bridge links
We determine a lower bound for the number of edges of a 2-connected maximal nontraceable graph, and present a construction of an infinite family of maximal nontraceable graphs that realize this bound.
We give examples showing that Kidwell's inequality for the maximal degree of the Brandt-Lickorish-Millett-Ho polynomial is in general not sharp.
We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several…
The canonical components of SL_2-character varieties of arithmetic two bridge link groups are determined.
Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge…
We show that every two-bridge knot $K$ of crossing number $N$ admits a polynomial parametrization $x=T_3(t), y = T_b(t), z =C(t)$ where $T_k(t)$ are the Chebyshev polynomials and $b+\deg C = 3N$. If $C (t)= T_c(t)$ is a Chebyshev…
In this paper we investigate the relationship between links in bridge position and plat presentations. We will show that the Hilden double coset classes of plat presentations of a link are equivalent to bridge positions of the link up to…
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
A differential geometric characterization of the braid-index of a link is found. After multiplication by 2pi, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper…
In this paper we give a simple proof of the equivalence between the rational link associated to the continued fraction $\left[ a_{1},a_{2},\cdots a_{m}\right],$ $a_{i}\in\mathbb{N}$, and the two bridge link of type $p/q,$ where $p/q$ is the…
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this…
This paper describes a method for the automatic evaluation of the Links-Gould two-variable polynomial link invariant (LG) for any link, given only a braid presentation. This method is currently feasible for the evaluation of LG for links…
We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating)…
We give necessary conditions for a polynomial to be the Conway polynomial of a two-bridge link. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley. We give a modulo 2 congruence for links, which…
Any 2-bridge knot in the 3-sphere has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.
We study factorizations of HOMFLY polynomials of certain knots and oriented links. We begin with a computer analysis of knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for…
We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms…
We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating links in thickened surfaces. It states that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating…