Circuit and fractional circuit covers of matroids

Let MM be a connected matroid having a ground set EE. Lemos and Oxley proved that |E(M)|≤12c(M)c∗(M) where c(M)c(M) (resp. c∗(M)c∗(M)) is the circumference (resp. cocircumference) of MM. In addition, they conjectured that one can find a collection of at most c∗(M)c∗(M) circuits which cover the elements of MM at least twice. In this paper, we verify this conjecture for regular matroids. Moreover, we show that a version of this conjecture is true for fractional circuit covers.