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- W2052803891 abstract "We give a lower bound for the treewidth of a graph in terms of the second smallest eigenvalue of its Laplacian matrix. We use this lower bound to show that the treewidth of a d-dimensional hypercube is at least ⌊3·2d/(2(d+4))⌋−1. The currently known upper bound is O(2d/d). We generalize this result to Hamming graphs. We also observe that every graph G on n vertices, with maximum degree Δ contains an induced cycle (chordless cycle) of length at least 1+logΔ(μn/8) (provided G is not acyclic), has a clique minor Kh for some h=Ω((nμ2/(Δ+2μ)2)1/3)," @default.
- W2052803891 created "2016-06-24" @default.
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- W2052803891 date "2003-08-01" @default.
- W2052803891 modified "2023-09-25" @default.
- W2052803891 title "A spectral lower bound for the treewidth of a graph and its consequences" @default.
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- W2052803891 doi "https://doi.org/10.1016/s0020-0190(03)00286-2" @default.
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