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  • ON THE DEFINITION OF GRAPH INDEX

  • Part of
  • A. STOIMENOW
  • Journal:
    Journal of the Australian Mathematical Society / Volume 94 / Issue 3 / June 2013
    Published online by Cambridge University Press:
    10 June 2013, pp. 417-429
    Print publication:
    June 2013
    • Article
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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.