5 problems

Let $G$ be a finite graph whose Hadwiger number is at most $h$, and let $f$ be a function. A composition factor of a group is a factor in a composition series of that group. Babai'…

Let $C\subset\mathbb{R}^{2}$ be a star-shaped Jordan region, meaning a bounded planar set homeomorphic to the unit disk and containing a point $x$ such that every segment joining…

Let $\mathcal{G}$ be a graph class. It is $(\operatorname{tw},\operatorname{had})$-bounded if there is a function $f$ such that…

A graph class has bounded Hadwiger number if there is a bound $h$ such that every graph in the class has Hadwiger number at most $h$. A simple group is represented by a graph if it…

Let $G_1,\ldots,G_r$ be graphs on a common vertex set of size $n$, whose edge sets partition the edges of $K_n$, and let $\ngpl{\eta}(r;n)$ denote the minimum of…