Geodesic
Large Degree Vertices in Longest Cycles of Graphs, I
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 363-382

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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.
Keywords: longest cycle, large degree vertices, order, connectivity, independent number 
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Li, Binlong; Xiong, Liming; Yin, Jun. Large Degree Vertices in Longest Cycles of Graphs, I. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 363-382. http://geodesic.mathdoc.fr/item/DMGT_2016_36_2_a8/