关于广义可传递竞赛多面体极值点的刻画

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.047

Konstantinos Papalamprou

引用次数: 0

摘要

一个非负的n×n矩阵[xij]被称为广义竞赛，记作GTT(n)，如果:xii=0(对于所有i)， xij+xji=1(对于所有(i,j)且i≠j)， 1≤xij+xjk+xki≤2(对于所有(i,j,k)且i,j,k成对不同)。在[9]中，利用与GTT矩阵相关的超图，证明了当n≤6时，GTT(n)多面体的所有顶点都是半积分。在这项工作中，我们证明了这些矩阵属于2正则矩阵类，并强调了相关的优化含义。最后，根据我们的方法和已知的部分结果，给出了n≥7时GTT(n)多面体极值点表征的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On characterizing the extreme points of the generalized transitive tournament polytope

A non-negative $n \times n$ matrix [ $x_{i j}$ ] is called generalized tournament, denoted GTT(n), if: $x_{i i} = 0$ (for all i), $x_{i j} + x_{j i} = 1$ (for all(i,j) with $i \neq j$ ) and $1 \leq x_{i j} + x_{j k} + x_{k i} \leq 2$ (for all (i,j,k) with $i, j, k$ pairwise distinct). In [9], using hypergraphs associated with GTT matrices, it has been shown that for $n \leq 6$ all the vertices of the GTT(n) polytope are half-integral. In this work, we show that these matrices belong to the class of 2-regular matrices and highlight the related optimization implications. Finally, based on our approach and known partial results, conjectures on characterizing the extreme points of the GTT(n) polytope for $n \geq 7$ are provided.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.