On n-connected minors of the es-splitting binary matroids
Abstract
The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor of rank-(r + 1) having |E(M)| + 1 elements.
Keywords
Full Text:
PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.2.3
References
H. Azanchiler, Extension of line-splitting operation from graphs to binary matroid, Lobachevskii J. Math., 24 (2006), 3-12.
H. Azanchiler, A characterization of the bases of line-splitting matroids, Lobachevskii J. Math., 26 (2007), 5–15.
Y.M. Borse and S.B. Dhotre, On connected splitting matroids, Southeast Asian Bull. Math., 34 (2010), 807–811.
S.B. Dhotre, P.P. Malavadkar, and M.M. Shikare, On 3-connected es-splitting binary matroids, Asian-European J. Math. 9 (1)(2016), 1650017-26.
K.V. Dalvi, Y.M. Borse, and M.M. Shikare, Forbidden-minors for graphic and cographic es-splitting matroids. Lobachevskii J. Math., 31 (1) (2010), 27–35.
O. Khormali, On the connectivity of k-distance graphs. Electron. J. Graph Theory Appl., 5 (1) (2017), 83–93.
P.P. Malavadkar, M.M. Shikare, and S.B. Dhotre, A characterization of n-connected splitting matroids, Asian-European J. Math., 7 (4)(2014), 1450060-7.
P.P. Malavadkar, M.M. Shikare, and S.B. Dhotre, A characterization of cocircuits of an essplitting matroid, J. Comb. Math. Comb. Comput., 105 (2018) 247–258.
J.G. Oxley, Matroid theory, Oxford University Press, Oxford (1992).
T.T. Raghunathan, M.M. Shikare, and B.N. Waphare, Splitting in a binary matroid, Discrete Math., 184 (1998), 267–271.
M.M. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull. Math., 32 (2008),151–159.
M.M. Shikare, S.B. Dhotre, and P.P. Malavadkar, A forbidden-minor characterization for the class of regular matroids which yield the cographic es-splitting matroids, Lobachevskii J. of
Math., 34 (2013), 173–180.
P.J. Slater, A Classification of 4-connected graphs, J. Combin. Theory, 17 (1974), 282–298.
W.T. Tutte, Connectivity in matroids, Canad. J. Math. 18 (1966), 1301–1324.
D.K. Wagner, Bipartite and Eulerian minors, European J. Combin., 74 (2018), 1–10.
D.J.A. Welsh, Euler and bipartite matroids, J. Combin. Theory, 6 (1969), 375–377.
Y. Wu, Even poset and a parity result for binary linear code, Linear Algebra Appl., 418 (2006), 591–594.
Refbacks
- There are currently no refbacks.
ISSN: 2338-2287
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.