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

Abstract

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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).

How to cite

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Kiran 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

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  1. [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. [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. [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. [4] F. Harary, Graph Theory (Addison-Wesley, Reading, 1969). 
  5. [5] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992). 
  6. [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. [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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