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
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