On the Equitable Choosability of the Disjoint Union of Stars

Equitable k-choosability is a list analogue of equitable k-coloring that was introduced by Kostochka et al. (J Graph Theory 44:166–177, 2003). It known if vertex disjoint graphs $$G_1$$ and $$G_2$$ are equitably k-choosable, the union may not be k-choosable. Given any $$m \in \mathbb {N}$$ values k for which $$K_{1,m}$$ k-choosable known. Also, complete characterization 2-choosable With these facts in mind, we study choosability $$\sum _{i=1}^n K_{1,m_i}$$ , n stars. We show determining whether choosable NP-complete when same two colors assigned to every vertex. completely determine stars (or $$n \ge 2$$ identical stars) 2-choosable, present results on arbitrary k.