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Hamiltonian cycles in n ‐extendable graphs
Author(s) -
Kawarabayashi Kenichi,
Ota Katsuhiro,
Saito Akira
Publication year - 2002
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.10050
Subject(s) - combinatorics , mathematics , factor critical graph , graph , hamiltonian path , discrete mathematics , line graph , graph power
A graph G of order at least 2 n +2 is said to be n ‐extendable if G has a perfect matching and every set of n independent edges extends to a perfect matching in G . We prove that every pair of nonadjacent vertices x and y in a connected n ‐extendable graph of order p satisfy deg G x +deg G y ≥ p − n − 1, then either G is hamiltonian or G is isomorphic to one of two exceptional graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 75–82, 2002