3 problems

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…

Let $G$ be any graph, and fix an ordering of the edges and vertices used in a total weighting. A total sequence $k$-list-weighting assigns to each edge and vertex a weight from its…

Let $G$ be a graph with no component isomorphic to $K_2$. Fix an ordering of $E(G)$. A sequence edge $k$-list-weighting assigns to each edge a weight from its independently assigne…