Edge disjoint Hamilton cycles in intersection graphs of bases of matroids (Q2848810)

The intersection graph \(G(M)\) for bases of a matroid \(M=(E,B)\) is a graph with vertex set \(B\) and edge set given by all elements \(xx'\) such that \(x\) and \(x'\) are in \(B\) and the cardinality of their intersection is not zero. In this paper authors prove that the intersection graph \(G(M)\) for bases of a simple matroid \(M\) with rank greater or equal than 2 has at least two edge-disjoint Hamilton cycles whenever it has at least 5 vertices.