Let φ be a 2-coloring of the elements of a matroid M.The bicolor basis graph of M is the graph G(B(M), φ) with vertex set given by the set of bases of M in which two bases B and ~(B′) are adjacent if ~(B′)=(B-e)∪f for some elements e∈B and f∈ ~(B′) with φ(e)≠φ(f).Let M be a matroid with at least one circuit, we prove that G(B(M), φ) is connected for every 2-coloring φ of M if and only if M is a connected matroid.
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