On cocircuit covers of bicircular matroids

Abstract

AbstractGiven a graph G, one can define a matroid M=(E,C) on the edges E of G with circuits C where C is either the cycles of G or the bicycles of G. The former is called the cycle matroid of G and the latter the bicircular matroid of G. For each bicircular matroid B(G), we find a cocircuit cover of size at most the circumference of B(G) that contains every edge at least twice. This extends the result of Neumann-Lara, Rivera-Campo and Urrutia for graphic matroids