5 problems

Giant $d$-rigid component conjecture. If a subset satisfying these two conditions appears in $\mathcal G(n,p)$, then it a.a.s. induces a giant $d$-rigid component.

Local-first conjecture. Except for triangles and forests—and, for triangles, only in the unbiased game—the global reason for Maker's win appears no earlier than the local reason, w…

Consider the online power-of-choices geometric graph process on $n$ vertices, with radius … Here $c>0$, $f$ is a function from $(0,\infty)$ to $(0,1)$, and w.h.p. means with high p…

Fix $N\geq 1$. On the square lattice $(\mathbb{Z}^2,\mathbb{E}^2)$, assign independent uniform random variables $(\tau_e)_{e\in\mathbb{E}^2}$ to the edges. Starting with all edges…

Let $K_n$ be the complete graph on $n$ vertices, and let $\mathcal L(n,q)$ denote the largest component size that Waiter can force in Client's graph when playing a $(q:1)$ Waiter–C…