On the Excluded Minors for Regular Matroids which Yield Cographic Splitting Matroids

被引：1

作者：

Pirouz, Naiyer ^{[1
]}

Dalvi, Kiran ^{[2
]}

Shikare, M. M. ^{[1
]}

机构：

[1] Univ Pune, Dept Math, Pune 411007, Maharashtra, India

[2] Govt Coll Engn, Dept Math, Pune 411005, Maharashtra, India

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2011年 / 32卷 / 04期

关键词：

Binary matroid; regular matroid; cographic matroid; minor; splitting operation;

D O I：

10.1134/S1995080211040172

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. We obtain a forbidden minor characterization of a regular matroid M for which the splitting matroid M-x,M-y is cographic for every pair x, y of elements of M. This problem is solved by proving that there are exactly two minor-minimal graphs and one matrix which has R-10 as a minor does not have this property.

引用

页码：376 / 384

页数：9

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