On the Boolean dimension of a graph and other related parameters

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.

Keywords

• graphs
• boolean sum
• symplectic dimension
• geometric dimension
• tournaments
• inversion index
• 06a6, 06f15
• [math.math-co]mathematics [math]/combinatorics [math.co]