Skew-adjacency matrices of tournaments with bounded principal minors

被引：1
|
作者：
Boussairi, Abderrahim [1 ]
Ezzahir, Sara [1 ]
Lakhlifi, Soufiane [1 ]
Mahzoum, Soukaina [1 ]
机构：
[1] Hassan II Univ Casablanca, Fac Sci Ain Chock, Lab Math Fondamentales & Appl, Casablanca, Morocco
来源：
DISCRETE MATHEMATICS | 2023年 / 346卷 / 10期
关键词：
Tournament; Skew-adjacency matrix; Principal minor; Diamonds; Transitive blowup; ENERGY;
D O I：
10.1016/j.disc.2023.113552
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let T be a tournament with n vertices v1, ... , vn. The skew-adjacency matrix of T is the n x n zero-diagonal matrix S = [sij] in which sij = -sji =1 if vi dominates vj. It is well-known that the determinant of S is zero or the square of an odd integer. Moreover, the principal minors of S are at most 1 if and only if T is a local order. In this paper, we characterize the class of tournaments for which the principal minors of the skew-adjacency matrix do not exceed 9.& COPY; 2023 Elsevier B.V. All rights reserved.
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