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.
@article{bwmeta1.element.doi-10_7151_dmgt_1804,
author = {Jens-P. Bode and Anika Fricke and Arnfried Kemnitz},
title = {Improved Sufficient Conditions for Hamiltonian Properties},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {329-334},
zbl = {1311.05101},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1804}
}
Jens-P. Bode; Anika Fricke; Arnfried Kemnitz. Improved Sufficient Conditions for Hamiltonian Properties. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 329-334. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1804/
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