Large degree vertices in longest cycles of graphs, II

Binlong Li, Liming Xiong, Jun Yin

Abstract


In this paper, we consider the least integer d such that every k-connected graph G of order n (and of independent number α) has a longest cycle containing all vertices of degree at least d. We completely determine the d when k = 2. We propose a conjecture for those k-connected graph, where k ≥ 3.


Keywords


longest cycle, connectivity, independent number, large degree vertex

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.2.7

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ISSN: 2338-2287

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