A graph-theoretic approach to a partial order of knots and links

作者：Endo Toshiki; Itoh Tomoko; Taniyama Kouki^*

来源：Topology and Its Applications, 2010, 157(6): 1002-1010.

DOI：10.1016/j.topo1.2009.12.016

• Knot
• Link
• Partial order
• Planar graph
• Graph minor

We say that a link L(1) is an s-major of a link L(2) if any diagram of L(1) can be transformed into a diagram of L(2) by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by graph-theoretic methods.

• 出版日期2010-4-15