Youngsik Huh

AN ELEMENTARY SET FOR θn-CURVE PROJECTIONS

A finite set of nontrivial θn-curves is shown to be minimal among those which produce all projections of nontrivial θn-curves.

AN UPPER BOUND ON STICK NUMBER OF KNOTS

In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negamis upper bound to

Knots with small lattice stick numbers

s(K) \leq \frac{3}{2} (c(K)+1)

Identifiable projections of spatial graphs

. Moreover if K is a nonalternating prime knot, then

STRONGLY ALMOST TRIVIAL θ-CURVES

s(K) \leq \frac{3}{2} c(K)

STICK NUMBERS OF 2-BRIDGE KNOTS AND LINKS

.

Minimum lattice length and ropelength of 2-bridge knots and links

The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot

KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7 INTO ℝ3

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θ-CURVE POLYNOMIALS AND FINITE-TYPE INVARIANTS

and the figure-8 knot

Link lengths and their growth powers

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