# Forbidden-minor characterization for the class of cographic element splitting matroids

Kiran Dalvi; Y.M. Borse; M.M. Shikare

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 3, page 601-606
- ISSN: 2083-5892

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topKiran Dalvi, Y.M. Borse, and M.M. Shikare. "Forbidden-minor characterization for the class of cographic element splitting matroids." Discussiones Mathematicae Graph Theory 31.3 (2011): 601-606. <http://eudml.org/doc/270877>.

@article{KiranDalvi2011,

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).},

author = {Kiran Dalvi, Y.M. Borse, M.M. Shikare},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {binary matroid; graphic matroid; cographic matroid; minor},

language = {eng},

number = {3},

pages = {601-606},

title = {Forbidden-minor characterization for the class of cographic element splitting matroids},

url = {http://eudml.org/doc/270877},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Kiran Dalvi

AU - Y.M. Borse

AU - M.M. Shikare

TI - Forbidden-minor characterization for the class of cographic element splitting matroids

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 3

SP - 601

EP - 606

AB - 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).

LA - eng

KW - binary matroid; graphic matroid; cographic matroid; minor

UR - http://eudml.org/doc/270877

ER -

## References

top- [1] S. Akkari and J. Oxley, Some local extremal connectivity results for matroids, Combinatorics, Probability and Computing 2 (1993) 367-384, doi: 10.1017/S0963548300000766. Zbl0793.05033
- [2] Y.M. Borse, K. Dalvi and M.M. Shikare, Excluded-minor characterization for the class of cographic splitting matroids, Ars Combin., to appear. Zbl06475967
- [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. Zbl1194.05017
- [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. Zbl0955.05022
- [7] M.M. Shikare and B.N. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. 97 (2010) 111-127. Zbl1249.05048

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