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2009 | 29 | 3 | 629-644
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
29
Numer
3
Strony
629-644
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-10-15
poprawiono
2008-12-17
zaakceptowano
2008-12-17
Twórcy
autor
  • Department of Mathematics, Government College of Engineering, Pune 411 005, India
autor
  • Department of Mathematics, University of Pune, Pune 411 007, India
autor
  • Department of Mathematics, University of Pune, Pune 411 007, India
Bibliografia
  • [1] G. Azadi, Generalized splitting operation for binary matroids and related results (Ph.D. Thesis, University of Pune, 2001).
  • [2] Y.M. Borse, M.M. Shikare and Kiran Dalvi, Excluded-Minor characterization for the class of Cographic Splitting Matroids, Ars Combin., to appear.
  • [3] H. Fleischner, Eulerian Graphs and Related Topics, Part 1, Vol. 1 (North Holland, Amsterdam, 1990).
  • [4] A. Habib, Some new operations on matroids and related results (Ph.D. Thesis, University of Pune, 2005).
  • [5] F. Harary, Graph Theory (Addison-Wesley, Reading, 1969).
  • [6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).
  • [7] 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.
  • [8] A. Recski, Matroid Theory and Its Applications (Springer Verlag, Berlin, 1989).
  • [9] M.M. Shikare and G. Azadi, Determination of the bases of a splitting matroid, European J. Combin. 24 (2003) 45-52, doi: 10.1016/S0195-6698(02)00135-X.
  • [10] M.M. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull. Math. 32 (2007) 151-159.
  • [11] M.M. Shikare and B.N. Waphare, Excluded-Minors for the class of graphic splitting matroids, Ars Combin., to appear.
  • [12] P.J. Slater, A classification of 4-connected graphs, J. Combin. Theory 17 (1974) 281-298, doi: 10.1016/0095-8956(74)90034-3.
  • [13] W.T. Tutte, A theory of 3-connected graphs, Indag. Math. 23 (1961) 441-455.
  • [14] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1469
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