Tighter bounds on the independence number of the Birkhoff graph

The Birkhoff graph B n is the Cayley of symmetric group S , where two permutations are adjacent if they differ by a single cycle. Our main result tighter upper bound on independence number ? ( ) namely, we show that ? O ! / 1 . 9 7 improving previous known 2 Kane et al. (2017). approach combines higher-order version their representation theoretic techniques with linear programming. With an explicit construction, also improve lower factor This construction based new proper coloring which gives chromatic ? Via connections, implies alphabet size bounds for family maximally recoverable codes grid-like topologies.