Every graph is uniform-span $(2,2)$-choosable: Beyond the 1-2 conjecture

Kecai Deng, Hongyuan Qiu

For a simple graph $G=(V,E)$, a \emph{proper total weighting} is a mapping $w:V\cup E\to \mathbb{R}$ such that for every edge $uv\in E$, $w(u)+\sum_{e\ni u}w(e)\neq w(v)+\s…