He, Dongqi; Liu, Zhenhong; Tian, Feng An improvement of Bondy’s theorem on Hamilton graph condition. (English) Zbl 0986.05068 Adv. Math., Beijing 30, No. 1, 37-46 (2001). Let \(G= (V,E)\) be a graph. \(\sigma_k(G)\) is the minimum of the degree sum of every independent set of order \(k\) in \(G\). It is proved in this paper that a \(k\)-connected tough graph of order \(n\) contains a Hamilton circuit if \(\sigma_{k+1}(G)\) is at least \((k+1)(n-3)/2\). This result strengthens an early result of Bondy in 1980. Reviewer: Cun-Quan Zhang (Morgantown) MSC: 05C45 Eulerian and Hamiltonian graphs 05C38 Paths and cycles Keywords:circumference; connectivity; tough graph; Hamilton cycle PDFBibTeX XMLCite \textit{D. He} et al., Adv. Math., Beijing 30, No. 1, 37--46 (2001; Zbl 0986.05068)