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- W4317384009 abstract "We study the random planar graph process introduced by Gerke et al. [Random Structures Algorithms, 32 (2008), pp. 236–261]: Begin with an empty graph on vertices, consider the edges of the complete graph one by one in a random ordering, and at each step add an edge to a current graph only if the graph remains planar. They studied the number of edges added up to step for “large . In this paper we extend their results by determining the asymptotic number of edges added up to step in the early evolution of the process when . We also show that this result holds for a much more general class of graphs, including outerplanar graphs, planar graphs, and graphs on surfaces." @default.
- W4317384009 created "2023-01-19" @default.
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- W4317384009 date "2023-01-20" @default.
- W4317384009 modified "2023-10-18" @default.
- W4317384009 title "The Early Evolution of the Random Graph Process in Planar Graphs and Related Classes" @default.
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- W4317384009 doi "https://doi.org/10.1137/21m1450616" @default.
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