DMGT

Discussiones Mathematicae Graph Theory 31(3) (2011) 601-606
DOI: https://doi.org/10.7151/dmgt.1568

FORBIDDEN-MINOR CHARACTERIZATION FOR THE CLASS OF COGRAPHIC ELEMENT SPLITTING MATROIDS

Kiran Dalvi

Department of Mathematics
Government College of Engineering
Pune 411 005 India
e-mail: kiran_dalvi111@yahoo.com

Y.M. Borse and M.M. Shikare

Department of Mathematics
University of Pune
Pune 411 007 India
e-mail:ymborse11@gmail.com
e-mail:mms@math.unipune.ernet.in

Abstract

In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).

Keywords: binary matroid, graphic matroid, cographic matroid, minor.

2010 Mathematics Subject Classifications: 05B35.

References

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[2]	Y.M. Borse, K. Dalvi and M.M. Shikare, Excluded-minor characterization for the class of cographic splitting matroids, Ars Combin., to appear.
[3]	K. Dalvi, Y.M. Borse and M.M. Shikare, Forbidden-minor characterization for the class of graphic element splitting matroids, Discuss. Math. Graph Theory 29 (2009) 629-644, doi: 10.7151/dmgt.1469.
[4]	F. Harary, Graph Theory (Addison-Wesley, Reading, 1969).
[5]	J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).
[6]	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.
[7]	M.M. Shikare and B.N. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. 97 (2010) 111-127.

Received 14 January 2009
Revised 16 June 2010
Accepted 16 June 2010