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- W2115683609 abstract "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), Cioabă and Wong conjectured that for any integers k⩾2, d⩾2k and a d-regular graph G, if λ2(G)<d−2k−1d+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 λ2(G)<2δ−Δ−2k−1δ+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." @default.
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- W2115683609 date "2014-03-01" @default.
- W2115683609 modified "2023-10-16" @default.
- W2115683609 title "Edge-disjoint spanning trees and eigenvalues" @default.
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- W2115683609 doi "https://doi.org/10.1016/j.laa.2013.11.039" @default.
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