On the Boolean dimension of a graph and other related parameters
Maurice Pouzet (1) (2) (3), Hamza Si Kaddour (1) (2) (3), Bhalchandra Thatte (4) (5)
(1) Université Claude Bernard Lyon 1
(2) Institut Camille Jordan
(3) Combinatoire, théorie des nombres
(4) Universidade Federal de Minas Gerais = Federal University of Minas Gerais [Belo Horizonte, Brazil]
(5) Universidade Federal de Minas Gerais = Federal University of Minas Gerais
Abstract
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the Boolean dimension with the inversion index of a tournament.
