3 problems

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…

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 $t\geq 1$,