I’m faced with the following problem:

**Given**

- Directed and unweighted graph, where each edge E has two attributes

**Goal**

- Find every path through the 3 (or more) given edges

**Questions**

- Is it NP-hard?
- Is there already an algorithm for this?
- I was thinking about placing a node in every edge and than run Dijkstra algorithm to find the shortest path from A to B and then from B to C. Although, this complicates my graph. Any other ideas? Thanks