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Splitting operation and connectedness in binary matroids. (English) Zbl 0973.05017
Summary: In [T. T. Raghunathan, M. M. Shikare, and B. N. Waphare, Discrete Math. 184, No. 1-3, 267-271 (1998; Zbl 0955.05022)], the authors have extended the splitting operation of graphs to binary matroids. In this paper we explore the relationship between the splitting operation and connectedness in binary matroids. We prove that repeated applications of the splitting operation on a bridgeless disconnected binary matroid leads to a connected binary matroid. We extend the splitting lemma of graphs to binary matroids.
MSC:
05B35Matroids, geometric lattices (combinatorics)