Edge disjoint hamilton cycles in intersection graphs of bases of matroids - Zhang, Ying-Hao; Yu, Qinglin Roger; Liu, Gui-Zhen (Utilitas Mathematica, 2013)
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 GI(M) for bases of a simple matroid M with rank r(M) ≥ 2 has at least two edge-disjoint Hamilton cycles whenever |V(GI(M))| ≥ 5.