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An implicit degree condition for hamiltonian graphs

✍ Scribed by Hao Li; Wantao Ning; Junqing Cai

Book ID
113567627
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
216 KB
Volume
312
Category
Article
ISSN
0012-365X

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## Abstract For a positive integer __k__, a graph __G__ is __k‐ordered hamiltonian__ if for every ordered sequence of __k__ vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. It is shown that if __G__ is a graph of order __n__ with 3 ≀ __k__ ≀ __n

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## Abstract Let __G__ be a 2‐connected graph of order __n.__ We show that if for each pair of nonadjacent vertices __x__,__y__ ∈ __V(G)__, then __G__ is Hamiltonian.