Weighted proper orientations of trees and graphs of bounded treewidth

Júlio Araújo, Cláudia Linhares Sales, Ignasi Sau +1

Given a simple graph $G$, a weight function $w:E(G)\to \mathbb{N}\setminus \{0\}$, and an orientation $D$ of $G$, we define ${\mu }^{-}(D)={\max }_{v\in V(G)}{w}_D^{-}(v)$, where $w…