Abstract
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.
Research supported by the French ANR-project ”Graph decompositions and algorithms” (GRAAL).
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Kanté, M.M., Rao, M. (2010). Directed Rank-Width and Displit Decomposition. In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_19
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DOI: https://doi.org/10.1007/978-3-642-11409-0_19
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