Topological sorts on DAGs

In this article, we will study the topological sorts of two directed acyclic graphs (DAGs) and the associated properties. More specifically, we will study under what conditions a certain single (or some, or every) topological sort(s) of a DAG can be extended into the topological sort(s) of another DAG. We first give the necessary and sufficient conditions for the problems. We then indicate that these problems are solvable either in linear time cost or in the same time cost as to compute the transitive closure.