Here is the minimal counterexample to Tait's conjecture (about hamiltonian cycles), which has an order-2 automorphism group. http://mathworld.wolfram.com/Barnette-Bosak-LederbergGraph.html -- APG.
Sent: Wednesday, April 18, 2018 at 4:33 PM From: "Allan Wechsler" <acwacw@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Aubrey de Grey
The fact that the graph is so asymmetric gives me a strong intuition that it is nowhere near minimal.
On Wed, Apr 18, 2018 at 10:21 AM, James Buddenhagen <jbuddenh@gmail.com> wrote:
A nice image of the currently smallest known unit-distance graph with chromatic number 5 is here http://www.cs.utexas.edu/~marijn/CNP/826.pdf found by Marijn Heule. It has 826 vertices. For information see https://dustingmixon.wordpress.com/2018/04/14/polymath16-first-thread- simplifying-de-greys-graph/#comment-3867
On Tue, Apr 17, 2018 at 6:37 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Did you hear the exciting news that Aubrey de Grey has increased the lower bound on the chromatic number of the plane from 4 to 5?
https://cp4space.wordpress.com/2018/04/15/assorted-news-3/
The best upper bound is 7 (from colouring the cells of a hexagonal lattice of appropriate size). The previous lower bound of 4 is from the Moser's spindle.
Best wishes,
Adam P. Goucher
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