Geodesic
Graphs for n-circular matroids
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 437-447

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We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].
Keywords: matroid, matroidal family 
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Kawa, Renata. Graphs for n-circular matroids. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 437-447. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a6/