Geodesic
Forbidden-minor characterization for the class of graphic element splitting matroids
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 629-644.

Voir la notice de l'article provenant de la source Library of Science

This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solved by proving that there is exactly one minor-minimal matroid that does not have this property.
Keywords: binary matroid, graphic matroid, minor, splitting operation, element splitting operation 
@article{DMGT_2009_29_3_a12,
     author = {Dalvi, Kiran and Borse, M. and Shikare, M.},
     title = {Forbidden-minor characterization for the class of graphic element splitting matroids},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {629--644},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a12/}
}
TY  - JOUR
AU  - Dalvi, Kiran
AU  - Borse, M.
AU  - Shikare, M.
TI  - Forbidden-minor characterization for the class of graphic element splitting matroids
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2009
SP  - 629
EP  - 644
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a12/
LA  - en
ID  - DMGT_2009_29_3_a12
ER  - 
%0 Journal Article
%A Dalvi, Kiran
%A Borse, M.
%A Shikare, M.
%T Forbidden-minor characterization for the class of graphic element splitting matroids
%J Discussiones Mathematicae. Graph Theory
%D 2009
%P 629-644
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a12/
%G en
%F DMGT_2009_29_3_a12
Dalvi, Kiran; Borse, M.; Shikare, M. Forbidden-minor characterization for the class of graphic element splitting matroids. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 629-644. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a12/

[1] G. Azadi, Generalized splitting operation for binary matroids and related results (Ph.D. Thesis, University of Pune, 2001).

[2] Y.M. Borse, M.M. Shikare and Kiran Dalvi, Excluded-Minor characterization for the class of Cographic Splitting Matroids, Ars Combin., to appear.

[3] H. Fleischner, Eulerian Graphs and Related Topics, Part 1, Vol. 1 (North Holland, Amsterdam, 1990).

[4] A. Habib, Some new operations on matroids and related results (Ph.D. Thesis, University of Pune, 2005).

[5] F. Harary, Graph Theory (Addison-Wesley, Reading, 1969).

[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.

[8] A. Recski, Matroid Theory and Its Applications (Springer Verlag, Berlin, 1989).

[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.

[10] M.M. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull. Math. 32 (2007) 151-159.

[11] M.M. Shikare and B.N. Waphare, Excluded-Minors for the class of graphic splitting matroids, Ars Combin., to appear.

[12] P.J. Slater, A classification of 4-connected graphs, J. Combin. Theory 17 (1974) 281-298, doi: 10.1016/0095-8956(74)90034-3.

[13] W.T. Tutte, A theory of 3-connected graphs, Indag. Math. 23 (1961) 441-455.

[14] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976).