5 problems

Bollobás–Cooper–Fenner–Frieze conjecture. W.h.p., for every $t\geq\tau_k$, the graph $G_t^{(k)}$ spans $\left\lfloor\frac{k-1}{2}\right\rfloor$ edge-disjoint Hamilton cycles and, w…

Giant $d$-rigid component conjecture. Then a.a.s.:

$d$-rigid core threshold conjecture. At the same threshold probability

Van Vu's conjecture. Almost surely, the adjacency matrix of $\operatorname{core}_k(G)$ is non-singular.

A strongly regular graph has a parameter set $(v,k,a,c)$, where $v$ is the number of vertices, $k$ is the degree of each vertex, $a$ is the number of common neighbors for each pair…