Hamiltonian degree conditions which imply a graph is pancyclic
type: Item
instance of: scholarly article
title: Hamiltonian degree conditions which imply a graph is pancyclic
zbMATH Open document ID: 0698.05047
DOI: 10.1016/0095-8956(90)90133-K
author: D. Bauer
author: E. Schmeichel
published in: Journal of Combinatorial Theory. Series B
publication date: 1990-01-01T00:00:00Z
review text: Let G be a finite undirected graph without loops or multiple edges. Various sufficient degree conditions for such graphs to be Hamiltonian have been given by Chvatál, Fan and Bondy (propositions 1, 2, 3). In this paper it is shown that exactly each of the conditions in these propositions imply still more about the cycle structure of G. A n-vertex graph is said to be pancyclic if it contains a l-cycle for every l such that holds \(3\leq l\leq n.\) And by three main theorems it is proved that G is not only Hamiltonian but even either pancyclic, bipartite or a member of a certain family of exceptions. Going out from the propositions 1, 2, 3 the theorems are proved by using four interesting lemmas, the third of them especially describes further important properties of n-vertex graphs with Hamiltonian cycle.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 4144021
zbMATH Keywords: special cyclic structure of Hamiltonian graphs
reviewed by: Heinz-Joachim Presia
MaRDI profile type: Publication
cites work: The Geng-Hua Fan conditions for pancyclic or Hamilton-connected graphs
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cites work: On Hamilton's ideals
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full work available at URL: 0095-8956(90)90133-k
OpenAlex ID: W2082876092
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description: scientific article; zbMATH DE number 4144021