4 problems

Bounded nonrepetitive connection conjecture. There exists a constant $t$ such that every $2$-connected graph $G$ satisfies

Grytczuk's conjecture. There is a constant $c$ such that

A graph has page number $k$ if its vertices can be arranged on a spine and its edges partitioned into $k$ pages, with no two edges on the same page crossing in the spine order. A v…

Let $G$ be a graph. A vertex coloring is nonrepetitive if no path has a color sequence of the form $s_1,s_2,\dots,s_t,s_1,s_2,\dots,s_t$. Let $\pi(G)$ denote the minimum number of…