I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem.
(source: uci.edu)
broken image fixed (click 'rendered output' to see the difference; image retrieved via Wayback Machine); for more info, see https://meta.mathoverflow.net/a/4058/70594
Glorfindel
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I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem.
I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem.
(source: uci.edu)
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I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem.
alt text http://www.ics.uci.edu/%7Eeppstein/0xDE/knot-bounded-region-complexity.png
I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem. alt text http://www.ics.uci.edu/%7Eeppstein/0xDE/knot-bounded-region-complexity.png
I'm pretty sure something like the following construction can be used to transform any knot diagram into another diagram for the same knot in which each region has bounded complexity. I didn't draw the over-under relationships at the crossings but that's not a problem.
