Unfriendly partitions when avoiding vertices of finite degree

Leandro Fiorini Aurichi, Lucas Real

An unfriendly partition of a graph $G=(V,E)$ is a function $c:V\to 2$ such that $|\{x\in N(v):c(x)\ne c(v)\}|\ge |\{x\in N(v):c(x)=c(v)\}|$ for every vertex $v\in V$, where…