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Splitting in a binary matroid. (English) Zbl 0955.05022
Summary: We introduce a splitting operation for binary matroids which is a natural generalization of the splitting operation for graphs [{\it H. Fleischner}, Eulerian graphs and related topics. Part I, Volume 1 (Annals of Discrete Mathematics. 45. Amsterdam etc.: North-Holland) (1990; Zbl 0792.05091)] and investigate some of its basic properties. Eulerian binary matroids are characterized in terms of the splitting operation.

05B35Matroids, geometric lattices (combinatorics)
Full Text: DOI
[1] Fleischner, H.: Eulerian graphs. Selected topics in graph theory 2, 17-53 (1983)
[2] Fleischner, H.: Eulerian graphs and related topics. 1 (1990) · Zbl 0792.05091
[3] Oxley, J. G.: Matroid theory. (1992) · Zbl 0784.05002
[4] Recski, A.: Matroid theory and its applications. (1989) · Zbl 0729.05012
[5] Welsh, D. J. A.: Euler and bipartite matroids. J. combin. Theory 6, 375-377 (1969) · Zbl 0169.01901
[6] Welsh, D. J. A.: Matroid theory. (1976)
[7] Wilde, P. J.: The Euler circuit theorem for binary matroids. J. combin. Theory ser. B 18, 260-264 (1975) · Zbl 0321.05026