Geodesic
Characterizations of transversal and fundamental transversal matroids
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions of nonempty sets of cyclic flats. We prove counterparts, for fundamental transversal matroids, of this and other characterizations of transversal matroids. In particular, we show that fundamental transversal matroids are precisely the matroids that yield equality in Mason's inequalities and we deduce a characterization of fundamental transversal matroids due to Brylawski from this simpler characterization.
DOI : 10.37236/593
Classification : 05B35, 52B40
Mots-clés : Mason's inequalities 
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Joseph E. Bonin; Joseph P. S. Kung; Anna de Mier. Characterizations of transversal and fundamental transversal matroids. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/593

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