论文标题
$ g（n，p）$中的大麻的全球弹性
The global resilience of Hamiltonicity in $G(n, p)$
论文作者
论文摘要
用$ r_g（g，\ mathcal {h}）$表示图$ g $相对于汉密尔顿的全局弹性。也就是说，$ r_g（g，\ nathcal {h}）$是具有$ r $ edges的子graph $ h \ subseteq g $的最小$ r $，因此$ g \ setminus h $不是hamiltonian。我们表明，如果$ p $高于汉密尔顿阈值，而$ g \ sim g（n，p）$，则具有很高的概率，则$ r_g（g，\ m athcal {h}）=δ（g）-1 $。这很容易扩展到完整的间隔：对于[0,1] $中的每$ p（n）\，如果$ g \ sim g（n，p）$，则具有很高的概率，$ r_g（g，\ mathcal {h}）= \ max max \ \ \ \ \ \ \ \ {0，δ（g）（g）-1 \} $。
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 $H\subseteq G$ with $r$ edges, such that $G\setminus H$ is not Hamiltonian. We show that if $p$ is above the Hamiltonicity threshold and $G\sim G(n,p)$ then, with high probability, $r_g(G,\mathcal{H})=δ(G)-1$. This is easily extended to the full interval: for every $p(n)\in [0,1]$, if $G\sim G(n,p)$ then, with high probability, $r_g(G,\mathcal{H})= \max \{ 0,δ(G)-1 \}$.
