A Sufficient and Necessary Condition for Line Digraphs to Exist Hamilton Cycle and Hamilton Path

For a digraph D,the line digraph L(D) is the one whose vertex set is A(D) and the arcs set are the pairs {(xy,yz)},where xy∈A(D),yz∈A(D).In this paper,we prove that a connected line digraph L(D) exists Hamilton cycle if it contains a cycle factor,and exists Hamilton path if it contains a 1-path-cycle factor.