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Paths, Cycles and Connectivity

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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

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)