5 problems

Guo–Kang–Zwaneveld conjecture. For every graph $G$ and every integer $d\ge 0$,

Sittitrai–Pimpasalee's conjecture. If $d_1+d_2\geq 6$, then $G$ is $(d_1,d_2)$-colorable.

Let $c_k(2)$ denote the maximum integer $n$ such that every graph on $n$ vertices can be partitioned into two subsets, each of which is $k$-defective, and let $k\geq 0$ be an integ…

Let $R_1^{\mathcal{BIP}}(4,j)$ denote the 1-defective Ramsey number for bipartite graphs. Exceptional-case formula conjecture. For … one has … For all $j\geq 8$ outside this except…

Let $R_1^{\mathcal{PG}}(4,j)$ denote the 1-defective Ramsey number for perfect graphs, and let $j$ be a positive integer. Growth conjecture. There exists an integer $l\geq 3$ such…