3-6 Cage (false)

After lots of erasing and retries, I think I finally created a 3-6 Cage. The basis for my graph was two cycles of length 6, one in the shape of a hexagon and contained in that one was a twisted hexagon (4 edges cross, but do not have a joining vertex in the middle). From here, it was a process of elimination to figure out where the remaining edges could be placed. I will be presenting my graph to my adviser tomorrow to see if it is correct, but from the checks I’ve done, the girth is 6 and there are 14 vertices…which is the amount he told me the 6-3 cage is on.

cubic graph with girth 6 on 14 vertices

********** Later proved false, see this post ***********

 

  1. September 22nd, 2011

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