Abstract
At the 25th Manitoba Conference on Combinatorial Mathematics and Computing in Winnipeg 1995 Hartnell introduced the firefighter game modelling the containment of the spreading of an undesired property within a network. An initial configuration of the game consists of a pair (G, r) where G is a finite, simple, and undirected graph and r is a burned vertex of G. The game proceeds in rounds. In each round, first at most one vertex of G that is not burned is defended and then all vertices of G that are neither burned nor defended and have a burned neighbor are burned. Once a vertex is burned or defended, it remains so for the rest of the game. The game ends with the first round, in which no further vertex is burned. All vertices of G that are not burned at the end of the game are saved.
We acknowledge partial support by CNPq, CAPES, FAPERJ, and the CAPES DAAD Probral project “Cycles, Convexity, and Searching in Graphs”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2013 Scuola Normale Superiore Pisa
About this paper
Cite this paper
Costa, V., Dantas, S., Dourado, M.C., Penso, L.D., Rautenbach, D. (2013). Firefighting with general weights. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_101
Download citation
DOI: https://doi.org/10.1007/978-88-7642-475-5_101
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-474-8
Online ISBN: 978-88-7642-475-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)