F-rank-width of (edge-colored) graphs

Authors:
Mamadou Moustapha Kanté;Michael Rao
Affiliations:
Clermont-Université and Université Blaise Pascal, LIMOS, CNRS, France;CNRS, Laboratoire J.V. Poncelet, Moscow, Russia and Université de Bordeaux, LaBRI, CNRS, France
Venue:
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Year:
2011

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Abstract

Rank-width is a complexity measure equivalent to the clique-width of undirected graphs and has good algorithmic and structural properties. It is in particular related to the vertex-minor relation. We discuss an extension of the notion of rank-width to all types of graphs - directed or not, with edge colors or not -, named F-rank-width. We extend most of the results known for the rank-width of undirected graphs to the F-rank-width of graphs: cubic-time recognition algorithm, characterisation by excluded configurations under vertex-minor and pivot-minor, and algebraic characterisation by graph operations. We also show that the rank-width of undirected graphs is a special case of F-rank-width.