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- W4283775404 abstract "Denote by $r_g(G,mathcal{H})$ the global resilience of a graph $G$ with respect to Hamiltonicity. That is, $r_g(G,mathcal{H})$ is the minimal $r$ for which there exists a subgraph $Hsubseteq G$ with $r$ edges, such that $Gsetminus H$ is not Hamiltonian. We show that if $p$ is above the Hamiltonicity threshold and $Gsim G(n,p)$ then, with high probability, $r_g(G,mathcal{H})=delta (G)-1$. This is easily extended to the full interval: for every $p(n)in [0,1]$, if $Gsim G(n,p)$ then, with high probability, $r_g(G,mathcal{H})= max { 0,delta (G)-1 }$." @default.
- W4283775404 created "2022-07-03" @default.
- W4283775404 creator A5073871726 @default.
- W4283775404 date "2022-06-30" @default.
- W4283775404 modified "2023-10-16" @default.
- W4283775404 title "The global resilience of Hamiltonicity in $G(n, p)$" @default.
- W4283775404 doi "https://doi.org/10.48550/arxiv.2206.15235" @default.
- W4283775404 hasPublicationYear "2022" @default.
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