6 problems

Let $n$ be divisible by $3$ and let $G$ be a $K_4$-free graph on $n$ vertices. A balanced $3$-partition divides $V(G)$ into three classes of size $n/3$; class-edges are edges whose…

Let $n$ be even and let $G$ be a $K_4$-free graph on $n$ vertices. A balanced $2$-partition is a partition $V(G)=A\cup B$ with $|A|=|B|=n/2$. Balanced max-part conjecture for K4-fr…

For a graph $G$, let $D_2(G)$ be the minimum number of edges that must be deleted to make $G$ bipartite. Fix $r\geq3$, and let $G$ be an $n$-vertex $K_{r+1}$-free graph. Sudakov's…

Kr-free correspondence-cover packing conjecture. For every $r\ge3$, there is some $C_r>0$ such that the following holds for

Carlson et al.'s conjecture. Every $K_r$-free $d$-degenerate graph with $m$ edges has surplus

For each integer $k\ge 2$, let $d_k=d_k(K_k)$ denote the critical edge density of the complete graph $K_k$. Pfender's recurrence conjecture. The critical edge densities satisfy … T…