On A Characterization of Balanced Matroids

Balance has played an important role in the study of random graphs and matroids. A graph is balanced if its average degree is at least as large as the average degree of any of its subgraphs. The density of a non-empty loopless matroid is the number of elements of the matroid divided by its rank. A matroid is balanced if its density is at least as large as the density of any of its submatroids. Veerapadiyan and Arumugan obtained a characterization of balanced graphs; we extend their result to give a characterization of balanced matroids.