Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664061 | Acta Mathematica Scientia | 2012 | 9 Pages |
Abstract
The relationship between a link diagram and its corresponding planar graph is briefly reviewed. A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot. The relationship between planar graph and almost planar Seifert surface is discussed. Using planar graph, we construct an alternating amphicheiral prime knot with crossing number n for any even number n ≥ 4. This gives an affirmative answer to problem 1.66(B) on Kirby's problem list.
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