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...

Full description

Saved in:
Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. 23 no. 2, special issue...; no. Special issues
Main Authors: Pouzet, Maurice, Si Kaddour, Hamza, Thatte, Bhalchandra
Format: Journal Article
Language:English
Published: DMTCS 23.09.2022
Discrete Mathematics & Theoretical Computer Science
Subjects:
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 Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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