Disjoint directed triangles and quadrilaterals in directed graphs

Abstract

Let s > 1 and t > 1 be two integers and let D be a directed graph of order n > 3s + 4t. It is proved that if Δ(D) > (3n - 3)/2, then D contains s directed triangles and t directed quadrilaterals such that all of them are vertex disjoint. This theorem strengthens early results by Wang [H. Wang, Independent directed triangles in a directed graph, Graph and Combinatorics 16 (2000), 453-462] and Zhang and Wang [D. Zhang, H. Wang, Disjoint directed quadrilaterals in a directed graph, J. Graph Theory 50 (2005), 91- 104].