Abstract
From an integer valued function f we obtain, in a natural way, a matroid Mf on the domain of f. We show that the class M of matroids so obtained is closed under restriction, contraction, duality, truncation and elongation, but not under direct sum. We give an excluded-minor characterisation of M and show that M consists precisely of those transversal matroids with a presentation in which the sets in the presentation are nested. Finally, we show that on an n-set there are exactly 2n members of M.
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Zaslavsky, T. (2010). Voltage-Graphic Matroids. In: Barlotti, A. (eds) Matroid Theory and its Applications. C.I.M.E. Summer Schools, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11110-5_8
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DOI: https://doi.org/10.1007/978-3-642-11110-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11109-9
Online ISBN: 978-3-642-11110-5
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