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One sufficient condition for hamiltonian graphs
Author(s) -
Chen Guantao
Publication year - 1990
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.3190140414
Subject(s) - mathematics , combinatorics , hamiltonian path , hamiltonian (control theory) , discrete mathematics , indifference graph , graph , mathematical optimization
Let G be a 2‐connected graph of order n. We show that if\documentclass{article}\pagestyle{empty}\begin{document}$$ 2|{\rm N}({\rm X})\, \cup \,{\rm N}({\rm y})|\, + \,{\rm d}({\rm X})\, + \,{\rm d}({\rm y})\, \ge \,2{\rm n}\, - \,1 $$\end{document}for each pair of nonadjacent vertices x , y ∈ V(G) , then G is Hamiltonian.
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