Generalized theorem for simplicial maps between arbitrary graphs

Let $K$ and $G$ be arbitrary graphs, and let $\varphi:K\to G\subset\mathbb{R}^2$ be a simplicial map.

Generalized graph-map conjecture. Theorem~1.5 is true for $\varphi$.

This conjecture proposes extending the established criterion from the preceding theorem, which applies to graphs without vertices of degree greater than three, to arbitrary graphs. The supplied text gives no resolution status.