The crumby coloring conjecture for subcubic bipartite graphs

A crumby coloring is a red-blue vertex coloring in which the blue subgraph has maximum degree at most $1$ and the red subgraph has minimum degree at least $1$ and contains no path with $3$ edges. The bipartite crumby coloring conjecture. Every subcubic bipartite graph admits a crumby coloring. The conjecture concerns a broad bipartite subclass of subcubic graphs and is motivated by the failure of Thomassen's conjecture for some cubic graphs. Its resolution is not given in the source.