GANIAN, Robert, Petr HLINĚNÝ, Jaroslav NEŠETŘIL, Jan OBDRŽÁLEK a Patrice OSSONA DE MENDEZ. Shrub-depth: Capturing Height of Dense Graphs. Logical Methods in Computer Science. BRAUNSCHWEIG: LOGICAL METHODS COMPUTER SCIENCE E V, 2019, roč. 15, č. 1, s. "7:1"-"7:25", 25 s. ISSN 1860-5974. Dostupné z: https://dx.doi.org/10.23638/LMCS-15(1:7)2019. |
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@article{1646045, author = {Ganian, Robert and Hliněný, Petr and Nešetřil, Jaroslav and Obdržálek, Jan and Ossona de Mendez, Patrice}, article_location = {BRAUNSCHWEIG}, article_number = {1}, doi = {http://dx.doi.org/10.23638/LMCS-15(1:7)2019}, keywords = {tree-depth; clique-width; shrub-depth; MSO logic; transduction}, language = {eng}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, title = {Shrub-depth: Capturing Height of Dense Graphs}, url = {https://lmcs.episciences.org/5149}, volume = {15}, year = {2019} }
TY - JOUR ID - 1646045 AU - Ganian, Robert - Hliněný, Petr - Nešetřil, Jaroslav - Obdržálek, Jan - Ossona de Mendez, Patrice PY - 2019 TI - Shrub-depth: Capturing Height of Dense Graphs JF - Logical Methods in Computer Science VL - 15 IS - 1 SP - "7:1"-"7:25" EP - "7:1"-"7:25" PB - LOGICAL METHODS COMPUTER SCIENCE E V SN - 18605974 KW - tree-depth KW - clique-width KW - shrub-depth KW - MSO logic KW - transduction UR - https://lmcs.episciences.org/5149 L2 - https://lmcs.episciences.org/5149 N2 - 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. ER -
GANIAN, Robert, Petr HLINĚNÝ, Jaroslav NEŠETŘIL, Jan OBDRŽÁLEK a Patrice OSSONA DE MENDEZ. Shrub-depth: Capturing Height of Dense Graphs. \textit{Logical Methods in Computer Science}. BRAUNSCHWEIG: LOGICAL METHODS COMPUTER SCIENCE E V, 2019, roč.~15, č.~1, s.~''7:1''-''7:25'', 25 s. ISSN~1860-5974. Dostupné z: https://dx.doi.org/10.23638/LMCS-15(1:7)2019.
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