Definition: Hamiltonian Graph

A Hamiltionian graph is a simple graph \(G(V,E)\) that contains a Hamiltonian cycle.

  1. Lemma: Biconnectivity is a Necessary Condition for a Hamiltonian Graph
  2. Lemma: Dual Graph of a All Faces Contained in a Planar Hamiltonian Cycle is a Tree
  3. Theorem: Characterization of Planar Hamiltonian Graphs

Lemmas: 1 2
Proofs: 3 4 5 6
Theorems: 7 8

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  1. Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000