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)
引用
收藏
相关论文
共 50 条
  • [1] On the Boolean dimension of a graph and other related parameters
    Pouzet, Maurice
    Kaddour, Hamza Si
    Thatte, Bhalchandra D.
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2021, 23 (02):
  • [2] ON THE BOOLEAN METRIC DIMENSION OF A GRAPH
    MELTER, RA
    TOMESCU, I
    REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 1984, 29 (05): : 407 - 415
  • [3] Koszulness, Krull dimension, and other properties of graph-related algebras
    Alexandru Constantinescu
    Matteo Varbaro
    Journal of Algebraic Combinatorics, 2011, 34 : 375 - 400
  • [4] Koszulness, Krull dimension, and other properties of graph-related algebras
    Constantinescu, Alexandru
    Varbaro, Matteo
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2011, 34 (03) : 375 - 400
  • [5] Boolean approaches to graph embeddings related to VLSI
    Yanpei Liu
    Science in China Series A: Mathematics, 2001, 44 : 1034 - 1041
  • [6] Boolean approaches to graph embeddings related to VLSI
    刘彦佩
    Science China Mathematics, 2001, (08) : 1034 - 1041
  • [7] Boolean approaches to graph embeddings related to VLSI
    刘彦佩
    ScienceinChina,SerA., 2001, Ser.A.2001 (08) : 1034 - 1041
  • [8] Boolean approaches to graph embeddings related to VLSI
    Liu, YP
    SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2001, 44 (08): : 1034 - 1041
  • [9] BOOLEAN DIMENSION AND DIM-BOUNDEDNESS: PLANAR COVER GRAPH WITH A ZERO
    Blake, Heather Smith
    Micek, Piotr
    Trotter, William T.
    arXiv, 2022,
  • [10] Boolean Dimension of a Boolean Lattice
    Brianski, Marcin
    Hodor, Jedrzej
    La, Hoang
    Micek, Piotr
    Michno, Katzper
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2024,
12345