On the Boolean dimension of a graph and other related parameters

被引：0
|
作者：
Pouzet M. [1 ,2 ]
Kaddour H.S. [1 ]
Thatte B.D. [3 ]
机构：
[1] Univ. Lyon, Université Claude-Bernard Lyon1, CNRS UMR 5208, Institut Camille Jordan, 43, Bd. du 11 Novembre 1918, Villeurbanne
[2] Department of Mathematics and Statistics, University of Calgary, Calgary, AB
[3] Departamento de Matematica, Universidade Federal de Minas Gerais (UFMG), Av. Antonio Carlos, 6627, Caixa Postal 702, Região Pampulha, MG, Belo Horizonte
来源：
Discrete Mathematics and Theoretical Computer Science | 2022年 / 23卷 / 02期
关键词：
Boolean sum; geometric dimension; graphs; inversion index; symplectic dimension; tournaments;
D O I：
10.46298/dmtcs.7437
中图分类号：
O144 [集合论]; O157 [组合数学（组合学）];
学科分类号：
070104 ;
摘要：
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. © 2022 by the author(s)
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