6 problems

Chang–Huang–Zhu conjecture. Whenever $n\geq d+2$,

Let $G$ be a graph, and let $\mu(G)$ denote its Mycielski graph. A graph is semi-transitive if it admits an acyclic orientation with no shortcut. Hameed's conjecture. For every gra…

Let $G$ be a Hamiltonian-connected graph, meaning that there is a Hamiltonian path between every pair of vertices, and let $K_2$ denote the complete graph on two vertices. Mycielsk…

For integers $m\geq 3$, let $K_{m+1}$ be the complete graph on $m+1$ vertices, let $\mu_m(K_{m+1})$ be its $m$-Mycielskian, and let $\operatorname{im}(G)$ denote the largest $t$ su…

Iterated Mycielski labeling conjecture. For all $t\geq 1$,

Mycielski equality conjecture. For any graph $G$,