On the Minimal Crossing Number and the Braid Index of Links
Canadian journal of mathematics, Tome 45 (1993) no. 1, pp. 117-131

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1993-007-x
Mots-clés : 57M25, index of a graph, knot, link, the braid index, the minimal crossing number
Ohyama, Yoshiyuki. On the Minimal Crossing Number and the Braid Index of Links. Canadian journal of mathematics, Tome 45 (1993) no. 1, pp. 117-131. doi: 10.4153/CJM-1993-007-x
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[1] 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] 2. Berge, C., Graphs and hypergraphs, North-Holland Pub. Comp., 1973. Google Scholar

[3] 3. Burde, G. and Zieshung, H., Knots, de Guy ter, 1985. Google Scholar

[4] 4. Fox, R.H., On the total curvature of some tame knots, Ann. Math. 52(1950), 258–260. Google Scholar

[5] 5. Murasugi, K., Jones polynomials and classical conjectures in knot theory, Topology 26(1987), 187–194. Google Scholar

[6] 6. Murasugi, K., An estimate of the bridge index of links, Kobe J. Math. 5(1989), 75–86. Google Scholar

[7] 7. Murasugi, K., On the braid index of alternating links, Trans. Amer. Math. Soc, to appear. Google Scholar

[8] 8. Murasugi, K. and Przytycki, J.H., An index of a graph with applications to knot theory, preprint. Google Scholar

[9] 9. Rolfsen, D., Knots and links, Publish or Perish Inc., 1976. Google Scholar

[10] 10. Yamada, S., The minimal number of Seifert circles equals the braid index of a link, Inv. Math. 89(1987), 347–356. Google Scholar

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