On Connectivity of Basis Graph of Splitting Matroid

For a set C of circuits of a matroid M, B(M. C) is defined by the graph with one vertex foreach basis of M, in which two bases B_1 and B_2 are adjacent if B_1 ∪ B_2 contains exactly one circuit and this circuit lies in C. For two elements of a and b of ground set of a binary matroid M a splitting matroid M_{a.b} is constructed. It is specified by two collections of circuits C_0 and C_1 dependent with collections of circuits of M. We want to study connectivity of B(M_{{a.b}}. C_0) .

For a set C of circuits of a matroid M, B(M. C) is defined by the graph with one vertex foreach basis of M, in which two bases B_1 and B_2 are adjacent if B_1 ∪ B_2 contains exactly one circuit and this circuit lies in C. For two elements of a and b of ground set of a binary matroid M a splitting matroid M_{a.b} is constructed. It is specified by two collections of circuits C_0 and C_1 dependent with collections of circuits of M. We want to study connectivity of B(M_{{a.b}}. C_0) .