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- W2765360845 abstract "Let ${G_i}$ be the random graph process: starting with an empty graph $G_0$ with $n$ vertices, in every step $i geq 1$ 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, Komlos, and Szemeredi, and independently Bollobas, states that asymptotically almost surely the graph becomes Hamiltonian as soon as the minimum degree reaches $2$, that is if $delta(G_i) ge 2$ then $G_i$ is Hamiltonian. We establish a resilience version of this result. In particular, we show that the random graph process almost surely creates a sequence of graphs such that for $m geq (tfrac{1}{6} + o(1))nlog n$ edges, the $2$-core of the graph $G_m$ remains Hamiltonian even after an adversary removes $(tfrac{1}{2} - o(1))$-fraction of the edges incident to every vertex. A similar result is obtained for perfect matchings." @default.
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- W2765360845 date "2017-10-02" @default.
- W2765360845 modified "2023-09-27" @default.
- W2765360845 title "Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes" @default.
- W2765360845 hasPublicationYear "2017" @default.
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