8 problems

Let $G$ be an $n$-vertex graph whose edges are colored with $n$ colors, and let the rainbow girth be the minimum length of a rainbow cycle, with value $infty$ if no rainbow cycle e…

Let $G$ be an undirected graph, and let $F_1,F_2,\ldots,F_n$ be sets of edges in $G$. For a family of edge sets, let $rg(F_1,\ldots,F_n)$ denote the length of its shortest rainbow…

Let $S$ be a spectrum of rainbow cycle lengths, namely the set of cycle lengths occurring as rainbow cycles under a fixed edge-coloring. Spectrum regularity conjecture. The asympto…

Let $G^c$ be a strongly edge-colored graph with $n$ vertices, where strongly edge-colored means that any two adjacent edges and any two edges joined by an edge have distinct colors…

Let $G$ be an edge-colored graph of order $n$, and let $k$ be a positive integer. For a vertex $v$ of $G$, write $d^c(v)$ for its color degree, the number of distinct edge colors i…

Subset flip-graph rainbow-cycle conjecture. The flip graph $G_{n,k}^{\mathcal{C}}$ has a 1-rainbow cycle for all $2\leq k\leq n-2$.

Čada–Kaneko–Ryjáček conjecture. If

Alexeev's conjecture. For every $G$, the period $\per{\spec{G}}$ is a divisor of $4$.