A note on Hamiltonian circuits

@article{Chvtal1972ANO,
  title={A note on Hamiltonian circuits},
  author={V. Chv{\'a}tal and P. Erd{\"o}s},
  journal={Discret. Math.},
  year={1972},
  volume={2},
  pages={111-113}
}
Proof. Let G satisfy the hypothesis of Theorem 1. Clearly, G contains a circuit ; let C be the longest one . If G has no Hamiltonian circuit, there is a vertex x with x ~ C . Since G is s-connected, there are s paths starting at x and terminating in C which are pairwise disjoint apart from x and share with C just their terminal vertices x l, X2, . . ., x s (see [ 11, Theorem 1) . For each i = 1, 2, . . ., s, let y i be the successor of x i in a 
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References

SHOWING 1-3 OF 3 REFERENCES
Edge-disjoint Hamütonian circuits in graphs with vertices of large valency
  • 1971
Edge-disjoint Hamütonian circuits in graphs with vertices of large valency Studies in pure nuthemati s (papers presented to Richard Ratio)
  • Edge-disjoint Hamütonian circuits in graphs with vertices of large valency Studies in pure nuthemati s (papers presented to Richard Ratio)
  • 1971
C .R. Acad . Sci . Paris
  • C .R. Acad . Sci . Paris
  • 1960