Let hN,E, li, be a labeled directed graph, where N is a set of vertices, E NN is a set of edges, and l : E L is a function assigning labels from a set L to edges. Let source and target be functions on E such that source(s,t) = s and target(s,t) = t. Formulate the following properties formally:

1. Every label in L is a label of some edge.

2. There are no nodes that are target of more than two edges with identical labels.

3. There is at least one path of length three where all the edges have identical labels.

4. There are no nodes that are source of edges with more than two distinct labels.