2021/03/09 by Songling Shan, Shan, Songling
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2103.05146
openalex publication_date 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a t-tough graph on n≥ 3 vertices for some t>0. It was shown by Bauer et al. in 1995 that if the minimum degree of G is greater than (n)/(t+1)-1, then G is hamiltonian. In terms of Ore-type hamiltonicity conditions, the problem was only studied when t is between 1 and 2. In this paper, we show that if the degree sum of any two nonadjacent vertices of G is greater than (2n)/(t+1)+t-2, then G is hamiltonian.