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- Stephen Finbow, Andrew D. King, Gary MacGillivray, Romeo Rizzi
- Discrete Mathematics
- 2007

We show that the firefighter problem is NP-complete for trees of maximum degree three, but in P for graphs of maximum degree three if the fire breaks out at a vertex of degree at most two. © 2006… (More)

- Stephen Finbow, Gary MacGillivray
- Australasian J. Combinatorics
- 2009

The Firefighter Problem was introduced by Bert Hartnell in 1995 at the 25th Manitoba Conference on Combinatorial Mathematics and Computing [23]. Imagine that, at time 0, a fire breaks out at a vertex… (More)

- Wei-Fan Wang, Stephen Finbow, Ping Wang
- Theor. Comput. Sci.
- 2010

LetG be a connected network. Let k ≥ 1 be an integer. Suppose that a vertex v ofG becomes infected. A program is then installed on k-nodes not yet infected. Afterwards, the virus spreads to all its… (More)

- Nancy E. Clarke, Stephen Finbow, Shannon L. Fitzpatrick, Margaret-Ellen Messinger, Richard J. Nowakowski
- Australasian J. Combinatorics
- 2009

In the firefighting and the graph searching problems, a contaminate spreads relatively quickly. We introduce a new model, on directed acyclic graphs, in which the contamination spreads slowly. The… (More)

- Wei-Fan Wang, Stephen Finbow, Jiangxu Kong
- Theor. Comput. Sci.
- 2014

Article history: Received 29 November 2012 Received in revised form 16 May 2013 Accepted 21 May 2013 Communicated by D. Peleg

- Yuehua Bu, Stephen Finbow, Daphne Der-Fen Liu, Xuding Zhu
- Discrete Applied Mathematics
- 2014

Suppose G is a graph and H is a subgraph of G. Let L be a mapping that assigns to each vertex v of G a set L(v) of positive integers. We say (G, H) is backbone L-colourable if there is a proper… (More)

- Stephen Finbow, Margaret-Ellen Messinger, Martin F. van Bommel
- Australasian J. Combinatorics
- 2015

In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. After each attack, if the guards can “move” to form a dominating set that… (More)

- Nancy E. Clarke, Stephen Finbow, Shannon L. Fitzpatrick, Margaret-Ellen Messinger, Rebecca Milley, Richard J. Nowakowski
- Discrete Applied Mathematics
- 2016

A proper colouring is referred to as a Grundy colouring, or first-fit colouring if every vertex has a neighbour from each of the colour classes lower than its own. The Grundy number of a graph is the… (More)