# FAQ overflow

#### QUESTION

Again an edge-partitioning problem whose complexity I'm curious about, motivated by a previous question of mine.

Input: a cubic graph $G=(V,E)$

Question: is there a partition of $E$ into $E_1, E_2, \ldots, E_s$, such that the subgraph induced by each $E_i$ is either a claw (i.e. $K_{1,3}$, often called a star) or a $3$-path (i.e. $P_4$)?

I think I saw a paper one day where this problem was proven to be NP-complete, but I cannot find it anymore, and I don't remember whether that result applied to cubic graphs. On a related matter, I'm aware that edge-partitioning a bipartite graph into claws is NP-complete (see Dyer and Frieze). Does anyone have a reference for the problem I describe, or something related (i.e. the same problem on another graph class, that I could then try to reduce to cubic graphs)?