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

• Autorzy: Kiran Dalvi , Y.M. Borse , M.M. Shikare
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

binary matroid; graphic matroid; cographic matroid; minor

Kategorie tematyczne

• 05B35: Matroids, geometric lattices

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 3
• Strony: 601-606

Daty

wydano

2011

otrzymano

2009-01-14

poprawiono

2010-06-16

zaakceptowano

2010-06-16

Twórcy

autor

Kiran Dalvi

• Department of Mathematics, Government College of Engineering, Pune 411 005 India

autor

Y.M. Borse

• Department of Mathematics, University of Pune, Pune 411 007 India

autor

M.M. Shikare

• Department of Mathematics, University of Pune, Pune 411 007 India

Bibliografia

• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1568