Directed Path-width and Monotonicity in Digraph Searching |
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Authors: | János Barát |
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Institution: | (1) Department of Mathematics, Technical University of Denmark, B.303. 2800 Lyngby, Denmark |
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Abstract: | Directed path-width was defined by Reed, Thomas and Seymour around 1995. The author and P. Hajnal defined a cops-and-robber
game on digraphs in 2000. We prove that the two notions are closely related and for any digraph D, the corresponding graph parameters differ by at most one. The result is achieved using the mixed-search technique developed
by Bienstock and Seymour. A search is called monotone, in which the robber's territory never increases. We show that there
is a mixed-search of D with k cops if and only if there is a monotone mixed-search with k cops. For our cops-and-robber game we get a slightly weaker result: the monotonicity can be guaranteed by using at most one
extra cop.
On leave from Bolyai Institute, University of Szeged, Hungary. This research has been supported by a Marie Curie Fellowship
of the European Community under contract number HPMF-CT-2002-01868 and by OTKA Grants F.030737 and T.34475. |
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Keywords: | Search games Path-width Cops-and-robber games Monotonicity Directed graph |
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