8 problems

Let $G$ be a connected graph of chromatic number $k$, with $G\not\cong C_7$, where $C_7$ is the cycle of order $7$. A full $f$-rainbow path is a path whose vertices receive pairwis…

Let $G$ be a finite simple triangle-free graph, let $\chi(G)$ be its chromatic number, and let $\phi:V(G)\to[k]$ be a proper vertex coloring, where $k=\chi(G)$. A path in $G$ is ra…

Schrijver's conjecture. If $G$ is a properly edge-colored $d$-regular graph, then $G$ contains a rainbow path of length $d-1$.

Let $\Gamma$ be a finite Abelian group, and let $S\subseteq\Gamma\setminus\\{0\\}$. Call $S$ rearrangeable if its elements can be ordered so that all partial products are distinct.…

Let $a_1,\dots,a_d$ be distinct nonzero elements of $\mathbb{Z}_p$, where $p$ is prime, and suppose that … A rearrangement is an ordering $a_{i_1},\dots,a_{i_d}$ whose partial sums…

Let $G$ be a connected cubic graph of order $n$, and let ${\mathit{cp}}_4(G)$ denote the parameter measuring the minimum number of colors in a coloring of $G$ with no rainbow path…

Gallai-Ramsey reduction conjecture. For any graph $H$ with no isolated vertices, we have

Let $G$ be a connected $k$-chromatic graph. In a $k$-coloring, a certifying path is a path whose vertices meet the required distinct color classes, and call such a path forward or…