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Sep 29, 2015 at 19:18 review Late answers
Sep 29, 2015 at 20:11
Mar 16, 2013 at 15:56 comment added Andrew Woldar Brendan, you're correct. This is the same graph, only my model is constructed in a way that can be readily explained to, for example, a grad student who is not well versed in rank 2 groups of Lie type or generalized n-gons. I'm going to think more on this problem. I find it very intriguibg. One can reduce 7812 for sure, for example by constructing the polarity graph of the generalized hexagon, which introduces smaller cycles, but this merely cuts the verex set in half ... not the kind of numbers you're looking for. Cheers.
Mar 16, 2013 at 5:59 comment added Brendan McKay Hi Andrew, There is a generalized hexagon on 7812 vertices mentioned in one of my comments above. But I'm still hopeful that a very much smaller graph (maybe even less than 100 vertices) is possible if 4-cycles and 6-cycles are allowed.
Mar 16, 2013 at 4:59 history answered Andrew Woldar CC BY-SA 3.0