Paths, Cycles and Connectivity 

| |

1.Bipartite Graphs 

2.Definition: Hamiltonian Cycle 

3.Definition: Eulerian Tour 

4.Definition: Walks, Trails, and Paths 

5.Definition: Closed Walks, Closed Trails, and Cycles 

6.Definition: Connected and Disconnected Graphs, Bridges and Cutvertices 

7.Definition: Weakly and Strongly Connected Digraphs 

8.Algorithm: Get All Components of a Graph 

9.Definition: Connected Vertices 

10.Definition: Biconnected Graphs, \(k\)-Connected Graphs 

11.Definition: Semi-Eulerian Tour, Open Trail 

12.Definition: Semi-Hamiltonian Path 

13.Proposition: Connectivity Is an Equivalence Relation - Components Are a Partition of a Graph 

14.Algorithm: Get the Component Induced by Vertices Connected to a Given Vertex 

15.Algorithm: Get the Cut Vertices and Biconnected Components of a Connected Graph