Tait's minimal alternating diagram conjecture
A link diagram is alternating when its crossings alternate between overcrossing and undercrossing along every component; an alternating link is one admitting a reduced alternating diagram. For such a link, crossing number is the minimum number of crossings among all diagrams representing it.
Tait's conjecture. Every alternating link has an alternating diagram with minimal crossing number among all diagrams of that link.
This is one of Tait's classical conjectures about alternating links and crossing number. It was proved for alternating links through work on the Jones polynomial and the Tait graph.
References
Primary source
Abhijit Champanerkar and Ilya Kofman, “A survey on the Turaev genus of knots”, arXiv:1406.1945 (2014).
Additional references
2 papers in this index state this conjecture (2007–2014). The statement above is taken from the most recent of them; the others are arXiv:0704.1941.
Progress summary
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