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Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes
[article]
2018
arXiv
pre-print
Let {G_i} be the random graph process: starting with an empty graph G_0 with n vertices, in every step i ≥ 1 the graph G_i is formed by taking an edge chosen uniformly at random among the non-existing ones and adding it to the graph G_i - 1. The classical 'hitting-time' result of Ajtai, Komlós, and Szemerédi, and independently Bollobás, states that asymptotically almost surely the graph becomes Hamiltonian as soon as the minimum degree reaches 2, that is if δ(G_i) > 2 then G_i is Hamiltonian.
arXiv:1710.00799v3
fatcat:ldm7qiptwjhopjpnyghvvzhqma