Let　τ(G)　and　λ2(G)　be　the　maximum　number　of　edge-disjoint　spanning　trees　and　the　second　largest　eigenvalue　of　a　graph　G,　respectively.　Motivated　by　a　question　of　Seymour　on　the　relationship　between　eigenvalues　of　a　graph　G　and　τ(G),　Cioabǎ　and　Wong　conjectured　that　for　any　integers　k≥2,　d≥2k　and　a　d-regular　graph　G,　if　λ2(G)<d-2k-1/d+1,　then　τ(G)≥k.　They　proved　this　conjecture　for　k=2,3.　Gu,　Lai,　Li　and　Yao　generalized　this　conjecture　to　simple　graph　and　conjectured　that　for　any　integer　k≥2　and　a　graph　G　with　minimum　degree　δ　and　maximum　degree　Δ,　if　lambda;2(G)　<2δ-Δ-2k-1/δ+1　then　τ(G)≥k.　In　this　paper,　we　prove　that　λ2(G)≤δ-2k-2/kδ+1　implies　τ(G)≥k　and　show　the　two　conjectures　hold　for　sufficiently　large　n.　©　2013　Elsevier　Inc.　All　rights　reserved.