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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 [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.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices

Citations:

Zbl 0792.05091
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References:

[1] Fleischner, H., Eulerian Graphs, (Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory, 2 (1983), Academic Press: Academic Press London), 17-53 · Zbl 0522.05041
[2] Fleischner, H., (Eulerian Graphs and Related Topics, vol. 1 (1990), North Holland: North Holland Amsterdam), Part 1 · Zbl 0792.05091
[3] Oxley, J. G., Matroid Theory (1992), Oxford University Press: Oxford University Press Oxford · Zbl 0784.05002
[4] Recski, A., Matroid Theory and its Applications (1989), Springer: Springer London · 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), Academic Press: Academic Press London · Zbl 0343.05002
[7] Wilde, P. J., The Euler circuit theorem for binary matroids, J. Combin. Theory Ser. B, 18, 260-264 (1975) · Zbl 0321.05026
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