Shifted Chvátal-resilience conjecture for Hamilton cycles in random graphs

Let $G=G_{n,p}$ be a random graph, and let $(\boldsymbol{\varepsilon},\boldsymbol{\delta})$-Chvátal-resilience mean resilience with respect to subgraphs satisfying the shifted Chvátal degree condition: there is an ordering $v_1,\ldots,v_n$ with $d_H(v_1)\geq\cdots\geq d_H(v_n)$ such that, for every $i<n/2$, either

$$d_H(v_i)\leq (n-i)p-\boldsymbol{\varepsilon}np$$

or

$$d_H(v_{n-i-\boldsymbol{\delta} n})\leq ip-\boldsymbol{\varepsilon}np.$$

Shifted Chvátal-resilience conjecture. For every $\varepsilon>0$, there exists $C>0$ such that, for $p\geq C\log n/n$, a.a.s. the random graph $G_{n,p}$ is $(\varepsilon,\varepsilon)$-Chvátal-resilient with respect to Hamiltonicity.

This conjecture proposes the Hamilton-cycle analogue of the preceding theorem for perfect matchings, extending Chvátal-type resilience to Hamiltonicity in sparse random graphs. Its resolution status is not specified in the supplied text.