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Cleaning with Brooms

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Abstract

A model for cleaning a graph with brushes was recently introduced. Most of the existing papers consider the minimum number of brushes needed to clean a given graph G in this model, the so-called brush number b(G). In this paper, we focus on the broom number, B(G), that is, the maximum number of brushes that can be used to clean a graph G in this model.

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References

  1. Alon N., Prałat P., Wormald N.: Cleaning regular graphs with brushes. SIAM J. Discrete Math. 23, 233–250 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alon, N., Spencer, J.H.: The Probabilistic Method. Wiley, New York (1992) (3rd edn, 2008)

  3. Biedl T., Chan T., Ganjali Y., Hajiaghayi M., Wood D.: Balanced vertex-orderings of graphs. Discrete Appl. Math. 148(1), 27–48 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gaspers S., Messinger M.-E., Nowakowski R., Prałat P.: Clean the graph before you draw it!. Inf. Process. Lett. 109, 463–467 (2009)

    Article  MATH  Google Scholar 

  5. Gaspers S., Messinger M.-E., Nowakowski R., Prałat P.: Parallel cleaning of a network with brushes. Discrete Appl. Math. 158(5), 467–478 (2009)

    Article  Google Scholar 

  6. Hobbs, B., Kahabka, J.: Underwater cleaning technique used for removal of Zebra mussels at the Fitzpatrick nuclear power plant. In: Proceedings of the Fifth International Zebra Mussel and Other Aquatic Nuisance Organisms Conference. The Sea Grant Nonindigenous Species Site. http://www.sgnis.org/publicat/47.htm. Accessed 4 June 2008 (1995)

  7. Kára J., Kratochvíl J., Wood D.: On the complexity of the balanced vertex ordering problem. Discrete Math. Theor. Comput. Sci. 9(1), 193–202 (2007)

    MATH  MathSciNet  Google Scholar 

  8. Kotler, S.R., Mallen, E.C., Tammus, K.M.: Robotic removal of Zebra mussel accumulations in a nuclear power plant screenhouse. In: Proceedings of the Fifth International Zebra Mussel and Other Aquatic Nuisance Organisms Conference. The Sea Grant Nonindigenous Species Site. http://www.sgnis.org/publicat/113.htm. Accessed 4 June 2008 (1995)

  9. Messinger, M.-E.: Methods of decontaminating networks. PhD thesis, Dalhousie University (2008)

  10. Messinger M.-E., Nowakowski R.J., Prałat P.: Cleaning a network with brushes. Theor. Comput. Sci. 399, 191–205 (2008)

    Article  MATH  Google Scholar 

  11. Messinger, M.-E., Nowakowski, R.J., Prałat, P., Wormald, N.: Cleaning random d-regular graphs with brushes using a degree-greedy algorithm. In: Proceedings of the 4th Workshop on Combinatorial and Algorithmic Aspects of Networking (CAAN 2007). Lecture Notes in Computer Science, vol. 4852, pp. 13–26. Springer, New York (2007)

  12. Meyer B.: Approaches to prevention, removal and killing of biofilms. Hygiene and disinfection. Int. Biodeterior. Biodegrad. 51(4), 249–253 (2003)

    Article  Google Scholar 

  13. Prałat, P.: Cleaning random d-regular graphs with Brooms. Graphs Comb. (submitted, 17 pp)

  14. Prałat P.: Cleaning random graphs with brushes. Australas. J. Comb. 43, 237–251 (2009)

    MATH  Google Scholar 

  15. Shearer J.: A note on bipartite subgraphs of triangle-free graphs. Random Struct. Algorithms 3, 223–226 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Margaret-Ellen Messinger

  2. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Richard J. Nowakowski

  3. Department of Mathematics, West Virginia University, Morgantown, WV, 26506-6310, USA

    Paweł Prałat

Authors
  1. Margaret-Ellen Messinger
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  2. Richard J. Nowakowski
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  3. Paweł Prałat
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Corresponding author

Correspondence to Paweł Prałat.

Additional information

Research partially supported by grants from NSERC and MITACS.

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Messinger, ME., Nowakowski, R.J. & Prałat, P. Cleaning with Brooms. Graphs and Combinatorics 27, 251–267 (2011). https://doi.org/10.1007/s00373-010-0965-2

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  • DOI: https://doi.org/10.1007/s00373-010-0965-2

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