Part: Paths, Cycles and Connectivity

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  1. Definition: Walks, Trails, and Paths
  2. Definition: Closed Walks, Closed Trails, and Cycles
  3. Chapter: Bipartite Graphs
  4. Definition: Hamiltonian Cycle
  5. Definition: Eulerian Tour
  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

Proofs: 1

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