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Discussiones Mathematicae Graph Theory 29(3) (2009) 629-644
DOI: https://doi.org/10.7151/dmgt.1469

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

Kiran Dalvi^*,  Y.M. Borse^**  and  M.M. Shikare^**

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

^**Department of Mathematics
University of Pune, Pune 411 007, India
e-mail: ymborse@math.unipune.ernet.in
e-mail: mms@math.unipune.ernet.in

Abstract

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.

2000 Mathematics Subject Classification: 05B35.

References

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Received 15 October 2008
Revised 17 December 2008
Accepted 17 December 2008