A minor-based characterization of matroid 3-connectivity

被引：3

作者：

Moss, Tyler ^{[1
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2013年 / 50卷 / 01期

关键词：

Matroid minor; 3-Connected matroid;

D O I：

10.1016/j.aam.2012.03.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that a matroid is 2-connected if and only if every 2-element set is contained in a circuit, or equivalently, a U-1,U-2-minor. This paper proves that a matroid is 3-connected if and only if every 4-element set is contained in a minor isomorphic to a wheel of rank 3 or 4; a whirl of rank 2, 3, or 4; or the relaxation of a rank-3 whirl. Some variants of this result are also discussed. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：132 / 141

页数：10