JOURNAL BROWSE
Search
Advanced SearchSearch Tips
KNOTS AND LINKS IN LINEAR EMBEDDINGS OF K6
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
KNOTS AND LINKS IN LINEAR EMBEDDINGS OF K6
Huh, Young-Sik; Jeon, Choon-Bae;
  PDF(new window)
 Abstract
We investigate the number of knots and links in linear embeddings of , the complete graph with 6 vertices. Concretely, we show that any linear embedding of contains either only one Hopf link, or three Hopf links and one trefoil knot.
 Keywords
trefoil knot;Hopf link;complete graph;linear embedding;
 Language
English
 Cited by
1.
STICK NUMBER OF THETA-CURVES,;;

호남수학학술지, 2009. vol.31. 1, pp.1-9 crossref(new window)
2.
HEPTAGONAL KNOTS AND RADON PARTITIONS,;

대한수학회지, 2011. vol.48. 2, pp.367-382 crossref(new window)
1.
On the number of links in a linearly embedded K3,3,1, Journal of Knot Theory and Its Ramifications, 2015, 24, 08, 1550041  crossref(new windwow)
2.
Linking number and writhe in random linear embeddings of graphs, Journal of Mathematical Chemistry, 2016, 54, 5, 1117  crossref(new windwow)
3.
KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7INTO ℝ3, Journal of Knot Theory and Its Ramifications, 2012, 21, 14, 1250132  crossref(new windwow)
4.
A refinement of the Conway–Gordon theorems, Topology and its Applications, 2009, 156, 17, 2782  crossref(new windwow)
5.
QUADRISECANT APPROXIMATION OF HEXAGONAL TREFOIL KNOT, Journal of Knot Theory and Its Ramifications, 2011, 20, 12, 1685  crossref(new windwow)
6.
LINKING IN STRAIGHT-EDGE EMBEDDINGS OF K7, Journal of Knot Theory and Its Ramifications, 2010, 19, 11, 1431  crossref(new windwow)
7.
HEPTAGONAL KNOTS AND RADON PARTITIONS, Journal of the Korean Mathematical Society, 2011, 48, 2, 367  crossref(new windwow)
8.
STICK NUMBER OF THETA-CURVES, Honam Mathematical Journal, 2009, 31, 1, 1  crossref(new windwow)
9.
Linearly embedded graphs in 3–space with homotopically free exteriors, Algebraic & Geometric Topology, 2015, 15, 2, 1161  crossref(new windwow)
 References
1.
C. Adams, B. Brennan, D. Greilshemier, and A. Woo, Stick numbers and composition of knots and links, J. Knot Theory Ramifications 6 (1997), no. 2, 149-161 crossref(new window)

2.
J. H. Conway and C. MaA. Gordon, Knots and links in spatial graphs, J. Graph Theory 7 (1983), no. 4, 445-453 crossref(new window)

3.
G. T. Jin and H. S. Kim, Polygonal knots, J. Korean Math. Soc. 30 (1993), no. 2, 371-383

4.
J. R. Munkres, Topology, second edition, Prentice Hall, Inc. Upper Saddle river, NJ 07458, (2000)

5.
S. Negami, Ramsey theorems for knots, links and spatial graphs, Trans. Amer. Math. Soc. 324 (1991), no. 2, 527-541 crossref(new window)

6.
J. L. Ramfnez Alfonsfn, Spatial graphs and oriented matroids: the trefoil, Discrete Comput. Geom. 22 (1999), no. 1, 149-158 crossref(new window)

7.
R. Randell, An elementary invariant of knots, J. Knot Theory Ramifications 3 (1994), no. 3, 279-286 crossref(new window)