SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY

SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY

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,...

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Veröffentlicht in:Acta mathematica scientia 2012-03, Vol.32 (2), p.663-671
1. Verfasser: 程志云 高红铸
Format: Artikel
Sprache:eng
Schlagworte:
57M25
almost planar Seifert surface
alternating knot
amphicheiral knot
Construction
Graphs
Knot theory
Knots
Links
Lists
Planar graph
交叉数
偶数
充分必要条件
平面图形
应用
纽结理论
表面
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Beschreibung
Zusammenfassung: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 .
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60047-2