Fixing Numbers for Matroids

被引：2

作者：

Gordon, Gary ^{[1
]}

McNulty, Jennifer ^{[2
]}

Neudauer, Nancy Ann ^{[3
]}

机构：

[1] Lafayette Coll, Dept Math, Easton, PA 18042 USA

[2] Univ Montana, Dept Math Sci, Missoula, MT 59812 USA

[3] Univ Pacific, Dept Math & Comp Sci, Forest Grove, OR 97116 USA

来源：

GRAPHS AND COMBINATORICS | 2016年 / 32卷 / 01期

关键词：

Graphic matroid; Bicircular matroid; Automorphism; AUTOMORPHISMS; GRAPHS;

D O I：

10.1007/s00373-015-1540-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have interpretations through permutation groups, and we make this connection explicit.

引用

页码：133 / 146

页数：14

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