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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2022

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.
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Dates and versions

hal-03214095 , version 1 (30-04-2021)
hal-03214095 , version 2 (31-03-2022)
hal-03214095 , version 3 (29-08-2022)
hal-03214095 , version 4 (06-09-2022)

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Maurice Pouzet, Hamza Si Kaddour, Bhalchandra D Thatte. On the Boolean dimension of a graph and other related parameters. Discrete Mathematics and Theoretical Computer Science, 2022, vol. 23 no. 2, special issue in honour of Maurice Pouzet, ⟨10.46298/dmtcs.7437⟩. ⟨hal-03214095v4⟩
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