The intersection graph for bases of a matroid M = (E, B) is a graph G~I(M) with vertex set B and edge set {BB' : |B ∩ B'| ≠ 0, B, B' ∈ B}. In this paper, we prove that the intersection graph G~I(M) for bases of a simple matroid M with rank r(M) ≥ 2 has at least two edge-disjoint Hamilton cycles whenever |V(G~I(M))| ≥ 5.
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