In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.
@article{bwmeta1.element.doi-10_7151_dmgt_1861, author = {Binlong Li and Liming Xiong and Jun Yin}, title = {Large Degree Vertices in Longest Cycles of Graphs, I}, journal = {Discussiones Mathematicae Graph Theory}, volume = {36}, year = {2016}, pages = {363-382}, zbl = {1338.05136}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1861} }
Binlong Li; Liming Xiong; Jun Yin. Large Degree Vertices in Longest Cycles of Graphs, I. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 363-382. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1861/