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.

引用

页数：6

共 14 条

[1]

Babai L., 2000, Electron. J. Combin, V7, P25, DOI DOI 10.37236/1516

[2] On unimodular tournaments [J].