Graphic Splitting of Cographic Matroids

Naiyer Pirouz

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 1, page 95-104
  • ISSN: 2083-5892

Abstract

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In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.

How to cite

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Naiyer Pirouz. "Graphic Splitting of Cographic Matroids." Discussiones Mathematicae Graph Theory 35.1 (2015): 95-104. <http://eudml.org/doc/271233>.

@article{NaiyerPirouz2015,
abstract = {In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.},
author = {Naiyer Pirouz},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {binary matroid; graphic matroid; cographic matroid; minor; splitting operation},
language = {eng},
number = {1},
pages = {95-104},
title = {Graphic Splitting of Cographic Matroids},
url = {http://eudml.org/doc/271233},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Naiyer Pirouz
TI - Graphic Splitting of Cographic Matroids
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 95
EP - 104
AB - In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
LA - eng
KW - binary matroid; graphic matroid; cographic matroid; minor; splitting operation
UR - http://eudml.org/doc/271233
ER -

References

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  1. [1] Y.M. Borse, Forbidden-minors for splitting binary gammoids, Australas. J. Combin. 46 (2010) 307-314. Zbl1196.05018
  2. [2] Y.M. Borse, M.M. Shikare and K.V. Dalvi, Excluded-minors for the class of co- graphic splitting matroids, Ars Combin. 115 (2014) 219-237. Zbl06475967
  3. [3] H. Fleischner, Eulerian Graphs and Related Topics (North Holland, Amsterdam, 1990). Zbl0792.05091
  4. [4] F. Harary, Graph Theory (Addison-Wesley, 1969). 
  5. [5] A. Mills, On the cocircuits of a splitting matroid, Ars Combin. 89 (2008) 243-253. Zbl1224.05087
  6. [6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992). 
  7. [7] T.T. Raghunathan, M.M. Shikare and B.N. Waphare, Splitting in a binary matroid, Discrete Math. 184 (1998) 267-271. doi:10.1016/S0012-365X(97)00202-1[Crossref] Zbl0955.05022
  8. [8] M.M. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull. Math. 32 (2007) 151-159. 
  9. [9] M.M. Shikare and G. Azadi, Determination of the bases of a splitting matroid, European J. Combin. 24 (2003) 45-52. doi:10.1016/S0195-6698(02)00135-X[Crossref] Zbl1014.05018
  10. [10] M.M. Shikare and B.N. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. 97 (2010) 111-127. Zbl1249.05048
  11. [11] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976). 

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