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- W4286825225 abstract "We prove a `resilience' version of Dirac's theorem in the setting of random regular graphs. More precisely, we show that, whenever $d$ is sufficiently large compared to $varepsilon>0$, a.a.s. the following holds: let $G'$ be any subgraph of the random $n$-vertex $d$-regular graph $G_{n,d}$ with minimum degree at least $(1/2+varepsilon)d$. Then $G'$ is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. Our result is best possible: firstly, the condition that $d$ is large cannot be omitted, and secondly, the minimum degree bound cannot be improved." @default.
- W4286825225 created "2022-07-24" @default.
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- W4286825225 date "2019-03-12" @default.
- W4286825225 modified "2023-10-18" @default.
- W4286825225 title "Dirac's theorem for random regular graphs" @default.
- W4286825225 doi "https://doi.org/10.48550/arxiv.1903.05052" @default.
- W4286825225 hasPublicationYear "2019" @default.
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