The Namer-Claimer game, part 2

arXiv I’ve previously written about the Namer-Claimer game.  I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.  The upper bound makes use of randomness, but in a very controlled way.  Analysing a truly random strategy still seems like it will be very …

Minimalist designs

Ben Barber, Stefan Glock, Daniela Kühn, Allan Lo, Richard Montgomery, Deryk Osthus In Edge decompositions of graphs with high minimum degree, Daniela Kühn, Allan Lo, Deryk Osthus and I proved that the edge sets of sufficiently dense graphs satisfying necessary divisibility conditions could be partitioned into copies of an arbitrary graph .  This result has since …