Discrete Mathematics - Vol 3 | 2. Hamiltonian Circuit by Abraham | Learn Smarter
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2. Hamiltonian Circuit

The lecture discusses Hamiltonian circuits and paths, emphasizing their importance in graph theory. It introduces Dirac's and Ore's theorems as sufficient conditions for the existence of Hamiltonian circuits within graphs, highlighting the differences compared to Eulerian graphs. A thorough explanation of both sufficient conditions is provided, alongside proofs to enhance understanding of their application and limitations.

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Sections

  • 2.1

    Hamiltonian Circuit

    A Hamiltonian circuit is a path in a graph that visits each vertex exactly once, returning to the starting vertex, while a Hamiltonian path visits each vertex exactly once without needing to return.

    Learning Practice

  • 2.1.1

    Definition Of Hamiltonian Circuit And Hamiltonian Path

    This section introduces Hamiltonian circuits and paths, differentiating them from Euler circuits, and discusses Dirac’s and Ore’s theorems as sufficient conditions for the existence of Hamiltonian graphs.

    Learning Practice

  • 2.1.2

    Dirac's Theorem

    Dirac's Theorem provides a sufficient condition for the existence of Hamiltonian circuits in connected graphs, based on the vertices' degrees.

    Learning Practice

  • 2.1.3

    Ore's Condition

    This section discusses Ore's Condition, a key theorem related to the existence of Hamiltonian graphs, and differentiates it from Dirac's theorem.

    Learning Practice

  • 2.1.4

    Proof Of Ore's Theorem

    This section discusses Ore's Theorem, a sufficient condition for the existence of Hamiltonian circuits in graphs.

    Learning Practice

  • 2.1.5

    Critical Pair Of Vertices And Conclusion

    This section discusses Hamiltonian circuits and paths, exploring necessary and sufficient conditions for the existence of Hamiltonian graphs, specifically Dirac's theorem and Ore's theorem.

    Learning Practice

  • 2.2

    Summary And References

    This section discusses Hamiltonian circuits and paths, focusing on Dirac’s and Ore’s theorems as sufficient conditions for the existence of Hamiltonian graphs.

    Learning Practice

References

ch52.pdf

Class Notes

Memorization

What we have learnt

  • Hamiltonian circuits requir...
  • Dirac's theorem states that...
  • Ore's condition relates to ...

Final Test

Revision Tests