7 problems

Let $F$ be a forest on $n$ vertices, and let $\chi'_{\cup}(F)$ denote its union vertex-distinguishing edge chromatic number, where edge colors are sets and the union of the colors…

Let $G$ be a graph, and let $\mathcal{L}=\mathcal{L}$ be a collection of equal-sized lists, each of size $k$, indexed by the vertices $v eq 0$ of $G$. Choose a color from each vert…

3-dimensional Euclidean extension conjecture.

2-sphere extension conjecture.

Plane extension conjecture.

Circle extension conjecture.

Cycle extension conjecture.