193 research outputs found
The almost alternating diagrams of the trivial knot
Bankwitz characterized an alternating diagram representing the trivial knot.
A non-alternating diagram is called almost alternating if one crossing change
makes the diagram alternating. We characterize an almost alternaing diagram
representing the trivial knot. As a corollary we determine an unknotting number
one alternating knot with a property that the unknotting operation can be done
on its alternating diagram.Comment: 29 pages, 18 figure
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