A simple proof of the Murasugi and Kauffman theorems on alternating links (Q1118205)

Recently, several outstanding classical conjectures of Tait on alternating link diagrams were proved by \textit{L. H. Kauffman} [Topology 26, 395-407 (1987; Zbl 0622.57004)], \textit{K. Murasugi} [Topology 26, 187- 194 (1987; Zbl 0628.57004), Math. Proc. Camb. Philos. Soc. 102, 317-318 (1987; Zbl 0642.57006)], and \textit{M. B. Thistlethwaite} [Topology 26, 297-309 (1987; Zbl 0622.57003), ibid. 27, 311-318 (1988)] with the help of Jones or Kauffman polynomials. This paper under review gives simplified proofs of the above results and a slight generalization of one of them.