Digraph decompositions and monotonicity in digraph searching
نویسندگان
چکیده
منابع مشابه
Digraph Decompositions and Monotonicity in Digraph Searching
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...
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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 prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between a minimum amin and maximum amax, we define 'multifractal components' K^ a) of K, and show that they are fractals in the sense of Taylor. The dimension /(or) of K^ is computed from the data of the pro...
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A graph, consisting of undirected edges, can be represented as a sum of two digraphs, consisting of oppositely oriented directed edges. Gutman and Plath in [J. Serb. Chem. Soc. 66 (2001), 237–241] showed that for annulenes, the eigenvalue spectrum of the graph is equal to the sum of the eigenvalue spectra of respective two digraphs. Here we exhibit a number of other graphs with this property.
متن کاملOn the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
We place our focus on the gap between treewidth’s success in producing fixed-parameter polynomial algorithms for hard graph problems, and specifically Hamiltonian Circuit and Max Cut, and the failure of its directed variants (directed tree-width [9], DAG-width [11] and kelly-width [8]) to replicate it in the realm of digraphs. We answer the question of why this gap exists by giving two hardness...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2011.05.003