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.
@article{bwmeta1.element.doi-10_7151_dmgt_1782,
author = {Naiyer Pirouz},
title = {Graphic Splitting of Cographic Matroids},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {95-104},
zbl = {1307.05042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1782}
}
Naiyer Pirouz. Graphic Splitting of Cographic Matroids. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 95-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1782/
[1] Y.M. Borse, Forbidden-minors for splitting binary gammoids, Australas. J. Combin. 46 (2010) 307-314. | Zbl 1196.05018
[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. | Zbl 06475967
[3] H. Fleischner, Eulerian Graphs and Related Topics (North Holland, Amsterdam, 1990). | Zbl 0792.05091
[4] F. Harary, Graph Theory (Addison-Wesley, 1969).
[5] A. Mills, On the cocircuits of a splitting matroid, Ars Combin. 89 (2008) 243-253. | Zbl 1224.05087
[6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).
[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] | Zbl 0955.05022
[8] M.M. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull. Math. 32 (2007) 151-159.
[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] | Zbl 1014.05018
[10] M.M. Shikare and B.N. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. 97 (2010) 111-127. | Zbl 1249.05048
[11] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976).