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
  • [31] GRAPH FUNCTIONS OF BOOLEAN FUNCTIONS
    REISCHER, C
    SIMOVICI, DA
    IEEE TRANSACTIONS ON COMPUTERS, 1984, 33 (01) : 97 - 99
  • [32] Graph embedding in Boolean hypercube
    Fomina, E.
    Zakrevski, A.
    2006 INTERNATIONAL BALTIC ELECTRONICS CONFERENCE, PROCEEDINGS, 2006, : 131 - +
  • [33] ON THE CAPACITY OF BOOLEAN GRAPH FORMULAS
    GARGANO, L
    KORNER, J
    VACCARO, U
    GRAPHS AND COMBINATORICS, 1995, 11 (01) : 29 - 48
  • [34] Graph labelings in boolean lattices
    Egawa, Y
    Miyamoto, M
    ARS COMBINATORIA, 1999, 52 : 13 - 19
  • [35] On the Bit Graph of Boolean Vectors
    Maity, Sushobhan
    Bhuniya, A. K.
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2022, 46 (03) : 405 - 414
  • [36] DIMENSION OF BOOLEAN VALUED LATTICES AND RINGS
    ESPANOL, L
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1986, 42 (03) : 223 - 236
  • [37] The dimension of neighboring levels of the Boolean lattice
    Kostochka, AV
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1998, 14 (03): : 267 - 268
  • [38] DOMINATION NUMBERS ON THE COMPLEMENT OF THE BOOLEAN FUNCTION GRAPH OF A GRAPH
    Jankairaman, T. N.
    Muthammai, S.
    Bhanumathi, M.
    MATHEMATICA BOHEMICA, 2005, 130 (03): : 247 - 263
  • [39] The dimension of two levels of the Boolean lattice
    Kierstead, HA
    DISCRETE MATHEMATICS, 1999, 201 (1-3) : 141 - 155
  • [40] THE DIMENSION OF INTERIOR LEVELS OF THE BOOLEAN LATTICE
    HURLBERT, GH
    KOSTOCHKA, AV
    TALYSHEVA, LA
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1994, 11 (01): : 29 - 40
12345