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On k ‐ordered graphs
Author(s) -
Faudree Jill R.,
Faudree Ralph J.,
Gould Ronald J.,
Jacobson Michael S.,
Lesniak Linda
Publication year - 2000
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/1097-0118(200010)35:2<69::aid-jgt1>3.0.co;2-i
Subject(s) - combinatorics , mathematics , hamiltonian path , wheel graph , hamiltonian (control theory) , graph , discrete mathematics , graph power , line graph , mathematical optimization
Ng and Schultz [J Graph Theory 1 (1997), 45–57] introduced the idea of cycle orderability. For a positive integer k , a graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k‐ordered Hamiltonian . We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k ‐ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000
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