3 problems

Let $G$ be a complete $r$-partite graph, and let $mu_{\operatorname{int}}(G)$ denote its interval coloring impropriety. Impropriety conjecture for complete multipartite graphs. … T…

Let $G$ be a 2-tree, that is, a graph obtained from a triangle by repeatedly adding a new vertex adjacent to both endpoints of an existing edge. Let $\mu_{\operatorname{int}}(G)$ d…

Subdivision conjecture. If $G\in \mathfrak{N}$, then