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I added an additional reference, since this attribution is often given to both articles.
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Neil Hoffman
Neil Hoffman
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This is an answer to your second question. As noticed by Steve Bleiler in "A note on Unknotting number", the minimal crossing diagram for the two bridge knot 10_8 ((29,5) in two bridge notation) has unknotting number 3, while a 14 crossing diagram has unknotting number 2, which is the unknotting number of the knot.

EDIT: In looking at the literature, this observation is also attributed to Yasutaka Nakanishi, "Unknotting numbers and knot diagrams with the minimum crossings," Math. Sem. Notes Kobe Univ., 11(2):257–258, 1983.

This is an answer to your second question. As noticed by Steve Bleiler in "A note on Unknotting number", the minimal crossing diagram for the two bridge knot 10_8 ((29,5) in two bridge notation) has unknotting number 3, while a 14 crossing diagram has unknotting number 2, which is the unknotting number of the knot.

This is an answer to your second question. As noticed by Steve Bleiler in "A note on Unknotting number", the minimal crossing diagram for the two bridge knot 10_8 ((29,5) in two bridge notation) has unknotting number 3, while a 14 crossing diagram has unknotting number 2, which is the unknotting number of the knot.

EDIT: In looking at the literature, this observation is also attributed to Yasutaka Nakanishi, "Unknotting numbers and knot diagrams with the minimum crossings," Math. Sem. Notes Kobe Univ., 11(2):257–258, 1983.

Source Link
Neil Hoffman
Neil Hoffman
  • 5.3k
  • 1
  • 23
  • 48

This is an answer to your second question. As noticed by Steve Bleiler in "A note on Unknotting number", the minimal crossing diagram for the two bridge knot 10_8 ((29,5) in two bridge notation) has unknotting number 3, while a 14 crossing diagram has unknotting number 2, which is the unknotting number of the knot.