Cyclability of 3-connected graphs

Harkat-Benhamdine, Amel; Li, Hao; Tian, Feng

doi:10.1002/1097-0118(200007)34:3<191::aid-jgt1>3.0.co;2-v

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Comparing Theorem 2 To Other Results1

Introduction1

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Cited by 14 publications

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“…Li [10] proved the following theorem, which was conjectured by Li, Tian, and Xu [11]. (Harkat-Benhamadine, Li and Tian [9], and Li, Tian, and Xu [11] have already proven the case k = 3 and the case k = 4, respectively.) Theorem 4 (Li [10]).…”

Section: Comparing Theorem 2 To Other Resultsmentioning

confidence: 87%

A Degree Sum Condition on the Order, the Connectivity and the Independence Number for Hamiltonicity

Chiba

Furuya

Ozeki

et al. 2019

Electron. J. Combin.

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In [Graphs Combin. 24 (2008) 469-483.], the third author and the fifth author conjectured that if G is a k-connected graph such that σ k+1 (G) ≥ |V (G)| + κ(G) + (k − 2)(α(G) − 1), then G contains a Hamiltonian cycle, where σ k+1 (G), κ(G) and α(G) are the minimum degree sum of k + 1 independent vertices, the connectivity and the independence number of G, respectively. In * this paper, we settle this conjecture. This is an improvement of the result obtained by Li: If G is a k-connected graph such that σ k+1 (G) ≥ |V (G)| + (k − 1)(α(G) − 1), then G is Hamiltonian. The degree sum condition is best possible.

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