Bounded rank perturbations of regular pencils over arbitrary fields
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DOI: 10.1016/j.laa.2020.05.015
Abstract: Abstract In this paper we solve the bounded rank perturbation problem for regular pencils over arbitrary fields. The solution is obtained by reducing the problem to a row completion problem for matrix pencils. The result… read more here.
Keywords: regular pencils; rank perturbations; bounded rank; pencils arbitrary ... See more keywords
Isomorphism, canonization, and definability for graphs of bounded rank width
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DOI: 10.1145/3453943
Abstract: 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… read more here.
Keywords: bounded rank; isomorphism; graphs bounded; rank width ... See more keywords
Technical perspective: A logical step toward the graph isomorphism problem
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DOI: 10.1145/3453945
Abstract: Leman algorithm in its plain form solves the isomorphism problem for bounded-rank width graphs. In fact, the paper even goes the crucial step further to show that canonization can be solved in the logic corresponding… read more here.
Keywords: bounded rank; isomorphism problem; rank; rank width ... See more keywords