Pentagons and cycle coverings | Zendy

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Pentagons and cycle coverings

Author(s) -

Wang Hong

Publication year - 2007

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.20208

Subject(s) - combinatorics , mathematics , vertex (graph theory) , disjoint sets , path graph , graph , integer (computer science) , discrete mathematics , graph power , line graph , computer science , programming language

Let G be a graph of order n ≥ 5 k + 2, where k is a positive integer. Suppose that the minimum degree of G is at least ⌈( n + k )/2⌉. We show that G contains k pentagons and a path such that they are vertex‐disjoint and cover all the vertices of G . Moreover, if n ≥ 5 k + 7, then G contains k + 1 vertex‐disjoint cycles covering all the vertices of G such that k of them are pentagons. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 194–208, 2007

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