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Sequences, claws and cyclability of graphs
Author(s) -
Favaron Odile,
Flandrin Evelyne,
Li Hao,
Liu Yiping,
Tian Feng,
Wu Zhengsheng
Publication year - 1996
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/(sici)1097-0118(199604)21:4<357::aid-jgt1>3.0.co;2-o
Subject(s) - combinatorics , mathematics , claw , hamiltonian path , wheel graph , vertex (graph theory) , hamiltonian (control theory) , pancyclic graph , graph , discrete mathematics , chordal graph , graph power , line graph , 1 planar graph , mechanical engineering , mathematical optimization , engineering
A subset S of vertices of a graph G is called cyclable in G if there is in G some cycle containing all the vertices of S . We give two results on the cyclability of a vertex subset in graphs, one of which is related to “ hamiltonian‐nice‐sequence ” conditions and the other of which is related to “ claw‐free ” conditions. They imply many known results on hamiltonian graph theory. Moreover, the analogous results related to the hamilton‐connectivity or to the existence of dominating cycle are also given. © 1996 John Wiley & Sons, Inc.