On the vertex kk-path cover

A subset SS of vertices of a graph GG is called a vertex kk-path cover if every path of order kk in GG contains at least one vertex from SS. Denote by psi sub(k)(G) psi k(G) the minimum cardinality of a vertex kk-path cover in GG. In this paper, an upper bound for psi sub(3) psi 3 in graphs with a g...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 161; no. 13-14; pp. 1943 - 1949
Main Authors Bresar, Bostjan, Jakovac, Marko, Katrenic, Jan, Semanisin, Gabriel, Taranenko, Andrej
Format Journal Article
LanguageEnglish
Published 01.09.2013
Subjects
Asymptotic properties
Cartesian
Graphs
Lower bounds
Mathematical analysis
Upper bounds
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Summary:A subset SS of vertices of a graph GG is called a vertex kk-path cover if every path of order kk in GG contains at least one vertex from SS. Denote by psi sub(k)(G) psi k(G) the minimum cardinality of a vertex kk-path cover in GG. In this paper, an upper bound for psi sub(3) psi 3 in graphs with a given average degree is presented. A lower bound for psi sub(k) psi k of regular graphs is also proven. For grids, i.e. the Cartesian products of two paths, we give an asymptotically tight bound for psi sub(k) psi k and the exact value for psi sub(3) psi 3.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0166-218X
DOI:10.1016/j.dam.2013.02.024