Vol. 5, No. 4, 2012

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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