Directed Rank-Width and Displit Decomposition
نویسندگان
چکیده
Rank-width is a graph complexity measure that has many structural properties. It is known that the rank-width of an undirected graph is the maximum over all induced prime graphs with respect to split decomposition and an undirected graph has rank-width at most 1 if and only if it is a distance-hereditary graph. We are interested in an extension of these results to directed graphs. We give several characterizations of directed graphs of rank-width 1 and we prove that the rank-width of a directed graph is the maximum over all induced prime graphs with respect to displit decomposition, a new decomposition on directed graphs.
منابع مشابه
COMPUTATION OF LINEAR RANK-WIDTH Keywords: linear rank-width; rank-decomposition; path-decomposition; vertex-minor Internship at Limos, Clermont-Ferrand, supervised by
(1) It is equivalent to clique-width, a complexity measure introduced by Courcelle et al. [4], that generalises the well-known complexity measure tree-width introduced by Robertson and Seymour in their graph minors series. (2) It is algorithmically more interesting than clique-width because we can recognise in polynomial time graphs of rank-width at most k (for fixed k) (3) It shares with tree-...
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