Happy Passover to all our readers
On the way from Cambridge to Tel Aviv I had a splendid three hour visit to London (from Kings Cross to UCL and back), where I met my graduate student Gabriel Gendler and Freddie Illingworth from UCL. (Like Tim Gowers and Imre Leader but a few decades later, Freddie and Gabriel first met at an IMO.) Gabriel and Freddie told me about several striking things including the remarkable “glider” proof for showing that Kneser graphs, Schrijver graphs, and stable Kneser graphs are Hamiltonian. (These proofs settled old standing conjectures.) To quote Merino, Mütze, and Namrata:
“Our main technical innovation is to study cycles in Kneser graphs by a kinetic system of multiple gliders that move at different speeds and that interact over time, reminiscent of the gliders in Conway’s Game of Life.”
Here are relevant links:
- Arturo Merino, Torsten Mütze, and Namrata: Kneser graphs are Hamiltonian.
- Torsten Mütze and Namrata, Hamiltonicity of Schrijver graphs and stable Kneser graphs.
- (A forthcoming survey article in the Notices of the AMS) Torsten Mütze, On Hamilton cycles in graphs defined by intersecting set systems.
- Torsten Mütze, Gliders in Kneser graphs, Internet site.
- (While looking at 4. I discovered this very cool site) COS++: The combinatorial object server.
Combinatorics and more 