Edge disjoint hamilton cycles in intersection graphs of bases of matroids

Abstract

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.