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- W2023759496 abstract "A tree decomposition of a graph G is a family of subtrees whose edge sets partition the edge set of G. The arboricity, a ( G ), is a trivial lower bound of τ ( G ), the minimum number of trees in a tree decomposition. We prove that a ( G )= τ ( G ) for all regular graphs of order n and degree d ⩾⌊ n /2⌋. This bound is best possible. The proof uses higher edge-connectivities, which also provide sufficient conditions for a ( G )= τ ( G ) when d>2 n ." @default.
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- W2023759496 date "2000-03-01" @default.
- W2023759496 modified "2023-09-26" @default.
- W2023759496 title "Higher edge-connectivities and tree decompositions in regular graphs" @default.
- W2023759496 doi "https://doi.org/10.1016/s0012-365x(99)00314-3" @default.
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