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- W4308117500 abstract "In this note, we investigate the tree-depth and tree-width in a heterogeneous random graph obtained by including each edge $e_{ij}$ $(ineq j)$ of a complete graph $K_{n}$ over $n$ vertices independently with probability $p_{n}(e_{ij})$. When the sequence of edge probabilities satisfies some density assumptions, we show both tree-depth and tree-width are of linear size with high probability. Moreover, we extend the method to random weighted graphs with non-identical edge weights and capture the conditions under which with high probability the weighted tree-depth is bounded by a constant." @default.
- W4308117500 created "2022-11-08" @default.
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- W4308117500 date "2022-11-11" @default.
- W4308117500 modified "2023-10-14" @default.
- W4308117500 title "On the tree-depth and tree-width in heterogeneous random graphs" @default.
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- W4308117500 doi "https://doi.org/10.3792/pjaa.98.015" @default.
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