Induced star-triangle factors of graphs

An induced star-triangle factor of a graph G is a spanning subgraph F of G such that each component of F is an induced subgraph on the vertex set of that component and each component of F is a star (here star means either K_1,n, n ≥ 2 or K₂) or a triangle (cycle of length 3) in G. In this paper, we establish that every graph without isolated vertices admits an induced star-triangle factor in which any two leaves from different stars K_1,n (n ≥ 2) are non-adjacent.