Brushing without capacity restrictions

In graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. Various problems arise, such as determining the minimum number of brushes that are required to clean the entire graph. This number is called the brushing number. Here, we study a new variant of the brushing...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 170; pp. 33 - 45
Main Authors Bryant, Darryn, Francetić, Nevena, Gordinowicz, Przemysław, Pike, David A., Prałat, Paweł
Format Journal Article
LanguageEnglish
Published Elsevier B.V 19.06.2014
Subjects
Brush number
Brushes
Brushing
Cartesian
Cleaning
Directed path covering
Graphs
Lower bounds
Mathematical analysis
Network cleaning
Trees
Directed path covering
Brush number
Network cleaning
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2014.01.024

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Summary:In graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. Various problems arise, such as determining the minimum number of brushes that are required to clean the entire graph. This number is called the brushing number. Here, we study a new variant of the brushing problem in which one vertex is cleaned at a time, but more than one brush may traverse a dirty edge. In particular, we obtain results on the brushing number of Cartesian products of graphs and trees, as well as upper and lower bounds on the brushing number in the general case.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2014.01.024