On some conjectures on biclique graphs☆

被引：0
|
作者：
Liang, Yanfang [1 ]
Wu, Baoyindureng [1 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2024年 / 343卷
关键词：
Biclique; Biclique graph; Helly property;
D O I：
10.1016/j.dam.2023.10.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The biclique B of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph KB(G) of a graph G is the graph with the bicliques of G as its vertices where two vertices of KB(G) are adjacent if and only if they have a common vertex in G. In this paper, we disprove a conjecture of Groshaus and Montero concerning Helly property of biclique graphs (Groshaus and Montero, 2021) and two conjectures of Montero concerning vertex removal in biclique graphs (Montero, 2022). In addition, we confirm a conjecture of Montero about the structural characterization of biclique graphs in the same paper.(c) 2023 Elsevier B.V. All rights reserved.
引用
收藏
页码：184 / 190
页数：7
相关论文
共 50 条
  • [11] ON SOME CONJECTURES ON CUBIC 3-CONNECTED GRAPHS
    FOUQUET, JL
    THUILLIER, H
    DISCRETE MATHEMATICS, 1990, 80 (01) : 41 - 57
  • [12] BICLIQUE NEIGHBORHOOD POLYNOMIALS OF GRAPHS
    Lumpayao, Shiena Mae B.
    Rasid, Regimar A.
    ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2024, 41 (07): : 581 - 588
  • [13] Biclique-Helly Graphs
    Marina Groshaus
    Jayme L. Szwarcfiter
    Graphs and Combinatorics, 2007, 23 : 633 - 645
  • [14] Hereditary biclique-Helly graphs: recognition and maximal biclique enumeration
    Eguia, Martiniano
    Soulignac, Francisco J.
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2013, 15 (01): : 55 - 74
  • [15] SOME EIGENVALUE PROPERTIES IN GRAPHS (CONJECTURES OF GRAFFITI .2.)
    FAVARON, O
    MAHEO, M
    SACLE, JF
    DISCRETE MATHEMATICS, 1993, 111 (1-3) : 197 - 220
  • [16] Biclique-colouring verification complexity and biclique-colouring power graphs
    Macedo Filho, H. B.
    Dantas, S.
    Machado, R. C. S.
    Figueiredo, C. M. H.
    DISCRETE APPLIED MATHEMATICS, 2015, 192 : 65 - 76
  • [17] Some duality conjectures for finite graphs and their group theoretic consequences
    Gersten, SM
    Riley, TR
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2005, 48 : 389 - 421
  • [18] Biclique Graphs of K3-free Graphs and Bipartite Graphs
    Groshaus, Marina
    Guedes, Andre L. P.
    PROCEEDINGS OF THE XI LATIN AND AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, 2021, 195 : 230 - 238
  • [19] Fractional biclique covers and partitions of graphs
    Watts, Valerie L.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2006, 13 (01):
  • [20] POLYNOMIAL REPRESENTATIONS OF THE BICLIQUE NEIGHBORHOOD OF GRAPHS
    Artes Jr, Rosalio G.
    Abubakar, Al-Jayson U.
    Kamdon, Sisteta U.
    ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2023, 37 : 37 - 45
12345