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- W2744724561 abstract "Abstract For a fixed integer g ≥ 0 , let S g ( n , m ) be a graph chosen uniformly at random from all graphs with n vertices and m edges that are embeddable on the orientable surface Sg of genus g. We prove that the component structure of Sg(n, m) features two phase transitions. The first one is analogous to the emergence of the giant component in the classical Erdős-Renyi random graph G(n, m) at m ∼ n 2 second phase transition occurs at m ∼ n , when the giant component covers almost all vertices." @default.
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- W2744724561 date "2017-08-01" @default.
- W2744724561 modified "2023-09-25" @default.
- W2744724561 title "Evolution of the giant component in graphs on orientable surfaces" @default.
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- W2744724561 doi "https://doi.org/10.1016/j.endm.2017.07.024" @default.
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