如何找到有向图中2个特定顶点之间的所有可能路径中存在的顶点？

Question

How to find the common vertices in all possible routes between 2 specific vertices in a directed graph? At least one route exist is a prerequisite.

Answer 1

O(|V||E|) solution. A and B - end of routes.

1. Iterate over all vertices.
2. Remove vertex from graph.
3. Check that path exist from A to B (ie with DFS)
4. If path don't exist - vertex is common for all routes.

Answer 2

The only way a vertex will be in all possible paths is if it's a 'bottleneck' - all paths go through it because it's the only way to go.

You can determine which vertices are in this set by removing each from the graph and testing if there still exists a path through the graph. By removing the node, you're looking to see if this removes all viable paths from the source to the destination.

Answer 3

您可以对Bellman-Ford进行变形，以检查是否在所有可能性中都使用了顶点。

Answer 4

采取所有可能路线的交叉点。