An Implicit Degree Condition for Relative Length of Long Paths and Cycles in Graphs

For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any thr...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2016-06, Vol.32 (2), p.365-372
Main Authors: Cai, Jun-qing, Li, Hao
Format: Article
Language:English
Subjects:
Applications of Mathematics
Combinatorics
Computer Science
Discrete Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0561-1