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Hamiltonian N 2 ‐locally connected claw‐free graphs
Author(s) -
Lai HongJian,
Shao Yehong,
Zhan Mingquan
Publication year - 2005
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/jgt.20046
Subject(s) - combinatorics , mathematics , distance hereditary graph , conjecture , line graph , discrete mathematics , vertex (graph theory) , graph , cubic graph , claw , graph power , voltage graph , mechanical engineering , engineering
A graph G is N 2 ‐ locally connected if for every vertex ν in G , the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjáček conjectured that every 3‐connected N 2 ‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005
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