|
|||||
 |
|
|
|
|
|
The firefighter
problem for regular infinite directed grids
Daniel P. Biebighauser, Lise E. Holte and Ryan M. Wagner
Vol. 5 (2012), No. 4, 393–409
|
Abstract |
|
We investigate the firefighter problem for regular infinite directed grids. We provide a complete classification of these grids by dividing them into two categories: grids where a single outbreak of fire can be contained with one firefighter per time step and grids that require a second firefighter at some time step. We then investigate infinite directed grids where the degrees of a single vertex are different from the degrees of all other vertices in the grid. |
Keywords
fire, firefighter, containment strategy, directed graphs
|
Mathematical Subject Classification 2010
Primary: 05C20, 05C75
|
Milestones
Received: 10 November 2010
Revised: 22 August 2012
Accepted: 14 September 2012
Published: 14 June 2013
Communicated by Ann Trenk
|
Authors |
| Daniel P. Biebighauser | |
| Department of Mathematics Concordia College 901 8th Street South Moorhead, MN 56562 United States |
|
| Lise E. Holte | |
| Department of Mathematics North Carolina State University 2200 Hillsborough Street Raleigh, NC 27695 United States |
|
| Ryan M. Wagner | |
| Department of Mathematics Concordia College 901 8th Street South Moorhead, MN 56562 United States |
|
|
