Esperet, Louis, van den Heuvel, Jan ORCID: 0000-0003-0897-9148, Maffray, Frederic and Sipma, Felix
(2013)
*Fire containment in planar graphs.*
Journal of Graph Theory, 73 (3).
pp. 267-279.
ISSN 0364-9024

## Abstract

In a graph G, a fire starts at some vertex. At every time step, firefighters can protect up to k vertices, and then the fire spreads to all unprotected neighbors. The k-surviving rate of G is the expectation of the proportion of vertices that can be saved from the fire, if the starting vertex of the fire is chosen uniformly at random. For a given class of graphs , we are interested in the minimum value k such that for some constant and all , (i.e., such that linearly many vertices are expected to be saved in every graph from ). In this note, we prove that for planar graphs this minimum value is at most 4, and that it is precisely 2 for triangle-free planar graphs.

Item Type: | Article |
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Official URL: | http://onlinelibrary.wiley.com/journal/10.1002/(IS... |

Additional Information: | © 2013 Wiley Periodicals, Inc. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 17 Apr 2013 10:34 |

Last Modified: | 14 Sep 2024 05:49 |

Projects: | ANR-10-JCJC-HEREDIA |

Funders: | ANR Project HEREDIA, Centre national de la recherche scientifique |

URI: | http://eprints.lse.ac.uk/id/eprint/49691 |

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