6 problems

Let $G$ be a $d$-regular graph on $n$ vertices with $d>1$. An irregular edge weighting assigns real weights to the edges so that all vertices have distinct weighted degrees, and…

Let $G$ be a $d$-regular graph with $n$ vertices, where $d\geq 2$. Its irregularity strength $s(G)$ is the least positive integer $k$ for which there is a weighting…

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 $r\geq 2$ be an integer, and let $G$ be a graph with maximum degree $\Delta$ and without an isolated edge. Write $s_r(G)$ for the least number of colours needed in an edge-colo…

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…