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Edge-critical cops and robber in planar graphs.
- Source :
-
Discrete Mathematics . Aug2014, Vol. 329, p1-11. 11p. - Publication Year :
- 2014
-
Abstract
- Abstract: The problem is to determine the number of ‘cops’ needed to capture a ‘robber’ in a game in which the cops always know the location of the robber, and the cops and robber move alternately along edges of a reflexive graph. The cops capture the robber if one of them occupies the same vertex as the robber at any time in the game. A cop-win graph is one in which a single cop has a winning strategy. A graph is cop-win edge-critical with respect to edge addition (respectively, deletion) when the original graph is not cop-win, but the addition (deletion) of any edge results in a cop-win graph. In this paper, edge-critical planar graphs are characterized. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 329
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 96188302
- Full Text :
- https://doi.org/10.1016/j.disc.2014.03.006