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- W4287448525 abstract "We consider an inhomogeneous version of the Barak-Erdős graph, i.e. a directed Erdős-Rényi random graph on { 1 , … , n } with no loop. Given f a Riemann-integrable non-negative function on [ 0 , 1 ] 2 and γ > 0 , we define G ( n , f , γ ) as the random graph with vertex set { 1 , … , n } such that for each i < j the directed edge ( i , j ) is present with probability p i , j ( n ) = f ( i / n , j / n ) n γ , independently of any other edge. We denote by L n the length of the shortest path between vertices 1 and n , and take interest in the asymptotic behaviour of L n as n → ∞ ." @default.
- W4287448525 created "2022-07-25" @default.
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- W4287448525 date "2022-11-01" @default.
- W4287448525 modified "2023-10-01" @default.
- W4287448525 title "On the length of the shortest path in a sparse Barak–Erdős graph" @default.
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- W4287448525 doi "https://doi.org/10.1016/j.spl.2022.109634" @default.
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