Geodesic
Improved Sufficient Conditions for Hamiltonian Properties
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 2, pp. 329-334.

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In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Keywords: Hamiltonian, traceable, Hamiltonian-connected 
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Bode, Jens-P.; Fricke, Anika; Kemnitz, Arnfried. Improved Sufficient Conditions for Hamiltonian Properties. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 2, pp. 329-334. http://geodesic.mathdoc.fr/item/DMGT_2015_35_2_a10/

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