A generalization of the firefighter problem on z × z

Discrete Applied Mathematics

Volumn 156, Issue 5, 2008, Pages 730-745

  Ng, K L ^a   Raff, P ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Containment certificate; Firefighter problem; Graph

Indexed keywords

COMPUTATION THEORY; FINITE DIFFERENCE METHOD; NUMBER THEORY; NUMERICAL METHODS; TIME VARYING SYSTEMS;

CONTAINMENT CERTIFICATES; FIREFIGHTER PROBLEMS; GRID GRAPHS;

PROBLEM SOLVING;

EID: 39049111431     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.08.011     Document Type: Article

References (12)

1. M. Develin, S.G. Hartke, Fire containment in grids of dimension three and higher, Discrete Appl. Math., in press.
2. Finbow S., and Hartnell B.L. On designing a network to defend against random attacks of radius two. Networks 19 (1989) 771-792
3. P. Fogarty, Catching the fire on grids, M.Sc. Thesis, University of Vermont, 2003.
4. Gunther G., and Hartnell B.L. On m-connected and k-neighbour-connected graphs. Graph Theory Combin. Algorithms Appl. 2 (1991) 585-596
5. Gunther G., and Hartnell B.L. Graphs with isomorphic survivor graphs. Congr. Numer. 79 (1990) 69-77
6. Hartnell B.L. Firefighter! An application of domination. 24th Manitoba Conference on Combinatorial Mathematics and Computing (1995), University of Manitoba in Winnipeg, Canada
7. Hartnell B.L., and Kocay W. On minimal neighbourhood-connected graphs. Discrete Math. 92 (1991) 95-105
8. Hartnell B.L., and Li Q. Firefighting on trees: how bad is the greedy algorithm?. Congr. Numer. 145 (2000) 187-192
9. Hartnell B.L., Finbow S., Li Q., and Schmeisser K. On minimizing the effects of fire or a virus on a network. J. Combin. Math. Combin. Comput. 33 (2000) 311-322
10. MacGillivray G., and Wang P. On the firefighter problem. J. Combin. Math. Combin. Comput. 47 (2003) 83-96
11. G. MacGillivray, S. Finbow, A. King, R. Rizzi, The firefighter problem for graphs of maximum degree three, 2005, preprint.
12. Wang P., and Moeller S.A. Fire control on graphs. J. Combin. Math. Combin. Comput. 41 (2002) 19-34