Lecture 7

DFS numbering: we assign numbers in the order with which nodes “finish”.

• A node is finished when it backtracks; with a stack, it would be when the value is popped off the stack

DAG

• Topological Sort
  • “the point of this exercise is that you’re completely drunk”

Theorem: A digraph $G$ has a topological sort iff $G$ is a DAG.
Proof: FTSOC assume $G$ has a cycle $C=(x_0,\dots ,x_k)$.

We have $(x_0,x_k)\in E$ and so $d$

We have proven if $G$ has a topological sort, then $G$ must be a DAG.