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
收藏
页码：376 / 384
页数：9
相关论文
共 42 条
  • [1] Cographic Element Splitting Matroids of regular Matroids
    Pirouz, Naiyer
    Dalvi, Kiran
    Shikare, M. M.
    UTILITAS MATHEMATICA, 2016, 101 : 91 - 106
  • [2] EXCLUDED-MINOR CHARACTERIZATION FOR THE CLASS OF COGRAPHIC SPLITTING MATROIDS
    Borse, Y. M.
    Dalvi, Kiran
    Shikare, M. M.
    ARS COMBINATORIA, 2014, 115 : 219 - 237
  • [3] GRAPHIC SPLITTING OF COGRAPHIC MATROIDS
    Pirouz, Naiyer
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2015, 35 (01) : 95 - 104
  • [4] EXCLUDED-MINORS FOR THE CLASS OF GRAPHIC SPLITTING MATROIDS
    Shikare, M. M.
    Waphare, B. N.
    ARS COMBINATORIA, 2010, 97 : 111 - 127
  • [5] Forbidden-Minors for Graphic and Cographic es-Splitting Matroids
    Dalvi, Kiran Vishnupant
    Borse, Y. M.
    Shikare, M. M.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2010, 31 (01) : 27 - 35
  • [6] A CHARACTERIZATION OF GRAPHIC MATROIDS WHICH YIELD BIOGRAPHIC SPLITTINGS MATROIDS
    Borse, Y. M.
    Shikare, M. M.
    Pirouz, Naiyer
    ARS COMBINATORIA, 2015, 118 : 357 - 366
  • [7] An excluded minors method for infinite matroids
    Bowler, Nathan
    Carmesin, Johannes
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2018, 128 : 104 - 113
  • [8] Cographic Splitting of Graphic Matroids Using a Set with Three Elements
    Solanki, S. D.
    Mundhe, Ganesh
    Dhotre, S. B.
    GRAPHS AND COMBINATORICS, 2023, 39 (05)
  • [9] Cographic Splitting of Graphic Matroids Using a Set with Three Elements
    S. D. Solanki
    Ganesh Mundhe
    S. B. Dhotre
    Graphs and Combinatorics, 2023, 39
  • [10] On Regular Matroids Without Certain Minors
    Harville, Kayla
    Reid, Talmage J.
    Wu, Haidong
    ANNALS OF COMBINATORICS, 2015, 19 (01) : 153 - 170
12345