Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T09:57:02.545Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Minimal Crossing Number and the Braid Index of Links

Published online by Cambridge University Press:  20 November 2018

Yoshiyuki Ohyama
Yoshiyuki Ohyama*
Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku, Tokyo 169, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we prove an inequality that involves the minimal crossing number and the braid index of links by estimating Murasugi and Przytycki’s index for a planar bipartite graph.

Keywords

57M25index of a graphknotlinkthe braid indexthe minimal crossing number
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 117 - 131
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Alexander, J.W., A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U.S.A. 9(1923), 93–95.Google Scholar
2. Berge, C., Graphs and hypergraphs, North-Holland Pub. Comp., 1973.Google Scholar
3. Burde, G. and Zieshung, H., Knots, de Guy ter, 1985.Google Scholar
4. Fox, R.H., On the total curvature of some tame knots, Ann. Math. 52(1950), 258–260.Google Scholar
5. Murasugi, K., Jones polynomials and classical conjectures in knot theory, Topology 26(1987), 187–194.Google Scholar
6. Murasugi, K., An estimate of the bridge index of links, Kobe J. Math. 5(1989), 75–86.Google Scholar
7. Murasugi, K., On the braid index of alternating links, Trans. Amer. Math. Soc, to appear.Google Scholar
8. Murasugi, K. and Przytycki, J.H., An index of a graph with applications to knot theory, preprint.Google Scholar
9. Rolfsen, D., Knots and links, Publish or Perish Inc., 1976.Google Scholar
10. Yamada, S., The minimal number of Seifert circles equals the braid index of a link, Inv. Math. 89(1987), 347–356.Google Scholar