Acta mathematica scientia, Series B >
SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY
Received date: 2009-12-22
Revised date: 2010-09-02
Online published: 2012-03-20
Supported by
Supported by NSF 10671018 and NSF 11171025.
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.
CHENG Zhi-Yun , GAO Hong-Zhu . SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 663 -671 . DOI: 10.1016/S0252-9602(12)60047-2
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