2.5 Digraphs: Walks & Paths

Consider some graph that has 10 edges and 16 vertices.

1. What is the maximum possible length of a longest path in this graph?

   Exercise 1

    Text Response  Answer:10
   The maximum is obviously 10, because there are 10 edges that can be arranged in a path.

2. What is the minimum possible length of a longest path in this graph?

   Exercise 2

    Text Response  Answer:1
   CheckShow Answer
The minimum possible longest path can't be 0, because we have a non-zero number of edges. A graph with edges from the first 10 vertices to the 11th has only length 1 paths. Hence, the minimum longest path is 1.