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Abstract
For a graph G and an integer k, denote by Vk the set {v ε V(G)  d(v) ≥ k}. Veldman proved that if G is a 2connected 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 almostgeneralization of Jackson's Theorem that every 2connected kregular graph of order n with n ≤ 3k is hamiltonian. An alternative proof of an extension of Jackson's Theorem is also presented.
Original language  English 

Pages (fromto)  373385 
Number of pages  13 
Journal  Journal of graph theory 
Volume  17 
Issue number  3 
DOIs  
Publication status  Published  1993 
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Dive into the research topics of 'Cycles containing all vertices of maximum degree'. Together they form a unique fingerprint.Activities
 1 Oral presentation

Cycles containing all vertices of maximum degree
H.J. Veldman (Speaker)
9 Apr 1992Activity: Talk or presentation › Oral presentation