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

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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.
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[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