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ON THE DEFINITION OF GRAPH INDEX

Part of: Graph theory Low-dimensional topology

Published online by Cambridge University Press:  10 June 2013

A. STOIMENOW
A. STOIMENOW*
Affiliation:
Department of Mathematics, Keimyung University, Darseo-Gu, Dalgubeoldaero 2800, Daegu 704-701, Korea email stoimeno@stoimenov.net
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Abstract

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This paper discusses a flaw in Murasugi–Przytycki’s Memoir ‘An index of a graph with applications to knot theory’ [Mem. Amer. Math. Soc. 106 (1993)]. We point out and partly fix a gap occurring in the proof of Murasugi–Przytycki’s braid index inequalities involving the graph index. We explain why their notion of index fails to precisely reflect the reduction of Seifert circles by their diagram move, and redefine the index to account for that discrepancy.

Keywords

skein polynomialgraph indexbraid indexBennequin surface

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 3 , June 2013 , pp. 417 - 429
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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