Seifert circles, braid index and the algebraic crossing number

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Abstract

We introduce new operations reducing the number of Seifert circles in link diagrams of a special type. The operations are similar to one described in [Mem. Amer. Math. Soc. 508 (1993)] and [Math. Proc. Cambridge Philos. Soc. 111 (2) (1992) 273]. We discuss a conjecture about the number of Seifert circles that can be canceled by applying the operation repeatedly. We translate the problem into one belonging to graph theory. © 2004 Elsevier B.V. All rights reserved.

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Malešič, J., & Traczyk, P. (2005). Seifert circles, braid index and the algebraic crossing number. Topology and Its Applications, 153(2-3 SPEC. ISS.), 303–317. https://doi.org/10.1016/j.topol.2003.05.010

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