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- W2025903184 abstract "An independent set S of a graph G is said to be essential if S has a pair of vertices distance two apart in G. We prove that if every essential independent set S of order k ≥ 2 in a k-connected graph of order p satisfies max {deg v:v ϵ S} ≥ ½ p, then g is hamiltonian. This generalizes the result of Fan (J. Combinatorial Theory B37 (1984), 221–227). If we consider the essential independent sets of order k + 1 instead of k in the assumption of the above statement, we can no longer assure the existence a hamiltonian cycle. However, we can still give a lower bound to the length of a longest cycle. © 1996 John Wiley & Sons, Inc." @default.
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- W2025903184 date "1996-02-01" @default.
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- W2025903184 title "Essential independent sets and Hamiltonian cycles" @default.
- W2025903184 doi "https://doi.org/10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l" @default.
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