科研之友
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摘要
The Gordian graph is the graph with vertex set the set of knot types and edge set consisting of pairs of knots that have a diagram wherein they differ at a single crossing. The bridge number is a classical knot invariant that is a measure of the complexity of a knot. It can be refined by another, recently discovered, knot invariant known as "bridge distance." We show, using arguments that are almost entirely elementary, that each vertex of the Gordian graph is adjacent to a vertex having arbitrarily high bridge number and bridge distance.
- 出版日期2017-1
