6 problems

Near-perfect packing conjecture. If

Győri–Keszegh's conjecture. For every such graph $G$ and every greedy partition $P$,

Rainbow triangle-packing conjecture. The graph $K_n$ contains a rainbow subgraph that is a disjoint union of triangles covering all but at most $C$ vertices, for some absolute cons…

The 3/2 random-graph conjecture. For all $C>3/2$ and $G=G(n,m)$, with high probability,

Let $G$ be a graph on $n$ vertices, let $\overline{G}$ denote its complement, and define … where $\nu^*(G)$ is the fractional triangle-packing number of $G$. Near-bipartite stabili…

Let $G$ be a $K_4$-free graph on $n$ vertices with $t_2(n)+m$ edges, where $t_2(n)=\lfloor n^2/4\rfloor$ is the number of edges in the $2$-partite Turán graph on $n$ vertices. Edge…