On induced matchings

Abstract Let q ∗ (G) denote the minimum integer t for which E(G) can be partitioned into t induced matchings of G. Faudree et al. conjectured that q ∗ (G)⩽d 2 , if G is a bipartite graph and d is the maximum degree of G. In this note, we give an affirmative answer for d=3, the first nontrivial case of this conjecture.