Table of Contents
ISRN Discrete Mathematics
Volume 2012 (2012), Article ID 406147, 8 pages
http://dx.doi.org/10.5402/2012/406147
Research Article

Some Results Involving the Splitting Operation on Binary Matroids

Department of Mathematics, University of Pune, Pune 411007, India

Received 26 October 2012; Accepted 20 November 2012

Academic Editors: A. Kelarev, T. Prellberg, and W. Wallis

Copyright © 2012 Naiyer Pirouz and Maruti Mukinda Shikare. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Oxley, Matroid Theory, Oxford University Press, Oxford, UK, 1992.
  2. H. Fleischner, Eulerian Graphs and Related Topics, vol. 1, part 1, North-Holland Publishing Co., Amsterdam, The Netherlands, 1990. View at Zentralblatt MATH
  3. H. Fleischner, “Eulerian graphs,” in Selected Topics in Graph Theory, 2, L. Beineke and R. Wilson, Eds., pp. 17–53, Academic Press, London, UK, 1983. View at Google Scholar · View at Zentralblatt MATH
  4. W. T. Tutte, “A theory of 3-connected graphs,” Indagationes Mathematicae, vol. 23, pp. 441–455, 1961. View at Google Scholar
  5. P. J. Slater, “A classification of 4-connected graphs,” Journal of Combinatorial Theory B, vol. 17, pp. 281–298, 1974. View at Publisher · View at Google Scholar
  6. T. T. Raghunathan, M. M. Shikare, and B. N. Waphare, “Splitting in a binary matroid,” Discrete Mathematics, vol. 184, no. 1–3, pp. 267–271, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. M. M. Shikare and B. N. Waphare, “Excluded-minors for the class of graphic splitting matroids,” Ars Combinatoria, vol. 97, pp. 111–127, 2010. View at Google Scholar · View at Zentralblatt MATH
  8. M. M. Shikare, G. Azadi, and B. N. Waphare, “Generalized splitting operation for binary matroids and its applications,” The Journal of the Indian Mathematical Society, vol. 78, no. 1–4, pp. 145–154, 2011. View at Google Scholar · View at Zentralblatt MATH
  9. A. Recski and Verlag, Matroid Theory and Its Applications, Springer, Berlin, Germany, 1989.
  10. J. R. Edmonds, “Systems of distinct representative and linear algebra,” Journal of Research of National Bureau of Standards B, vol. 71, no. 4, pp. 241–245.
  11. D. J. A. Welsh, “Euler and bipartite matroids,” Journal of Combinatorial Theory, vol. 6, pp. 375–377, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH