Isomorphism, canonization, and definability for graphs of bounded rank width
Keyword(s):
We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.
2014 ◽
Vol Vol. 16 no. 2
(PRIMA 2013)
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Keyword(s):
2009 ◽
Vol 20
(03)
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pp. 479-499
2010 ◽
Vol 33
(2)
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pp. 300-304
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