On the Boolean dimension of a graph and other related parameters

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...

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Veröffentlicht in:Discrete mathematics and theoretical computer science Jg. 23 no. 2, special issue...; H. Special issues
Hauptverfasser: Pouzet, Maurice, Si Kaddour, Hamza, Thatte, Bhalchandra
Format: Journal Article
Sprache:Englisch
Veröffentlicht: DMTCS 23.09.2022
Discrete Mathematics & Theoretical Computer Science
Schlagworte:
06a6, 06f15
[math.math-co]mathematics [math]/combinatorics [math.co]
boolean sum
Combinatorics
geometric dimension
graphs
inversion index
Mathematics
symplectic dimension
tournaments
Boolean sum
geometric dimension
tournaments
graphs
symplectic dimension
inversion index
ISSN:1365-8050, 1462-7264, 1365-8050
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.7437