Digraph searching, directed vertex separation and directed pathwidth
نویسندگان
چکیده
منابع مشابه
Forbidden Directed Minors and Directed Pathwidth
Undirected graphs of pathwidth at most one are characterized by two forbidden minors i.e., (i) K3 the complete graph on three vertices and (ii) S2,2,2 the spider graph with three legs of length two each [BFKL87]. Directed pathwidth is a natural generalization of pathwidth to digraphs. In this paper, we prove that digraphs of directed pathwidth at most one are characterized by a finite number of...
متن کاملDirected Path-width and Monotonicity in Digraph Searching
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 monot...
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We consider generalisations of tree width to directed graphs, that attracted much attention in the last fifteen years. About their relative strength with respect to “bounded width in one measure implies bounded width in the other” many problems remain unsolved. Only some results separating directed width measures are known. We give an almost complete picture of this relation. For this, we consi...
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We consider monotonicity problems for graph searching games. Variants of these games – defined by the type of moves allowed for the players – have been found to be closely connected to graph decompositions and associated width measures such as pathor tree-width. Of particular interest is the question whether these games are monotone, i.e. whether the cops can catch a robber without ever allowin...
متن کاملStrong-mixed searching and pathwidth
In this paper, we propose a new search model, called strongmixed search, which is a generalization of the mixed search. We show that the strong-mixed search number of a graph equals the pathwidth of the graph. We also describe relationships between the strong-mixed search number and other search numbers.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.08.045