8 problems

Let $G$ be a $d$-regular graph on $n$ vertices, and let $s(G)$ be the least integer $k$ for which the edges of $G$ can be assigned weights from $\\{1,\dots,k\\}$ so that all result…

Let $G$ be a graph without a component isomorphic to $K_2$. For each $1\le i\le\Delta(G)$, let $n_i$ be the number of vertices of degree $i$, and define … The specific sequence irr…

Let $G$ be a graph. For each $1\le i\le \Delta(G)$, let $n_i$ be the number of vertices of degree $i$, and define … The general sequence irregularity strength conjecture. The gener…

Let $G$ be a simple graph on $n$ vertices with minimum degree $\delta\geq 1$ and no isolated edges. Define the irregularity strength $s(G)$ as the least positive integer $k$ for wh…

Let $r\geq 2$ be an integer, let $G$ be a graph with maximum degree $\Delta$, and let $\operatorname{ts}_r(G)$ denote its $r$-distant total irregularity strength. Asymptotic upper-…

Bača–Jendrol'–Miller–Ryan's conjecture. If $G\not\cong K_5$, then

Let $G$ be a graph with no component isomorphic to $K_2$. For each degree $i$, let $n_i$ be the number of vertices of degree $i$, let $\Delta(G)$ be the maximum degree, and define…

Irregularity strength conjecture. For every graph $G$, the value of $s(G)$ is equal to the lower bound $L(G)$ plus a constant independent of $G$.