Publication details

Shrub-depth: Capturing Height of Dense Graphs

Authors

GANIAN Robert HLINĚNÝ Petr NEŠETŘIL Jaroslav OBDRŽÁLEK Jan OSSONA DE MENDEZ Patrice

Year of publication 2019
Type Article in Periodical
Magazine / Source Logical Methods in Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web https://lmcs.episciences.org/5149
Doi http://dx.doi.org/10.23638/LMCS-15(1:7)2019
Keywords tree-depth; clique-width; shrub-depth; MSO logic; transduction
Description The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural question: is there an analogously useful "depth" notion also for dense graphs (say; one which is stable under graph complementation)? To this end, in a 2012 conference paper, a new notion of shrub-depth has been introduced, such that it is related to the established notion of clique-width in a similar way as tree-depth is related to tree-width. Since then shrub-depth has been successfully used in several research papers. Here we provide an in-depth review of the definition and basic properties of shrub-depth, and we focus on its logical aspects which turned out to be most useful. In particular, we use shrub-depth to give a characterization of the lower omega levels of the MSO1 transduction hierarchy of simple graphs.
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