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- W2119258255 abstract "For a graph G and an integer k, denote by Vk the set {v ∈ V(G) | d(v) ≥ k}. Veldman proved that if G is a 2-connected graph of order n with n ≤ 3k - 2 and |Vk| ≤ k, then G has a cycle containing all vertices of Vk. It is shown that the upper bound k on |Vk| is close to best possible in general. For the special case k = δ(G), it is conjectured that the condition |Vk| ≤ k can be omitted. Using a variation of Woodall's Hopping Lemma, the conjecture is proved under the additional condition that n ≤ 2δ(G) + δ(G) + 1. This result is an almost-generalization of Jackson's Theorem that every 2-connected k-regular graph of order n with n ≤ 3k is hamiltonian. An alternative proof of an extension of Jackson's Theorem is also presented. © 1993 John Wiley & Sons, Inc." @default.
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- W2119258255 date "1993-07-01" @default.
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- W2119258255 title "Cycles containing all vertices of maximum degree" @default.
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- W2119258255 doi "https://doi.org/10.1002/jgt.3190170311" @default.
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