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@inproceedings{992004,
author = {Ganian, Robert and Hliněný, Petr and Obdržálek, Jan and Nešetřil, Jaroslav and Ossona de Mendez, Patrice and Ramadurai, Reshma},
address = {Německo},
booktitle = {Math Foundations of Computer Science MFCS 2012},
doi = {http://dx.doi.org/10.1007/978-3-642-32589-2_38},
edition = {7464},
keywords = {tree-depth; shrub-depth; MSO model checking},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Německo},
isbn = {978-3-642-32588-5},
pages = {419-430},
publisher = {Lecture Notes in Computer Science, Springer-Verlag},
title = {When Trees Grow Low: Shrubs and Fast MSO1},
year = {2012}
}
TY - JOUR
ID - 992004
AU - Ganian, Robert - Hliněný, Petr - Obdržálek, Jan - Nešetřil, Jaroslav - Ossona de Mendez, Patrice - Ramadurai, Reshma
PY - 2012
TI - When Trees Grow Low: Shrubs and Fast MSO1
PB - Lecture Notes in Computer Science, Springer-Verlag
CY - Německo
SN - 9783642325885
KW - tree-depth
KW - shrub-depth
KW - MSO model checking
N2 - Recent characterization [9] of those graphs for which coloured MSO2 model checking is fast raised the interest in the graph invariant called tree-depth. Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class. To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes the graph classes having interpretation in coloured trees of bounded height. We also introduce a common extension of cographs and of graphs with bounded shrub-depth - m-partite cographs (still of bounded clique-width), which are well quasi-ordered by the relation “is an induced subgraph of” and therefore allow polynomial time testing of hereditary properties.
ER -
GANIAN, Robert, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Jaroslav NEŠETŘIL, Patrice OSSONA DE MENDEZ and Reshma RAMADURAI. When Trees Grow Low: Shrubs and Fast MSO1. In \textit{Math Foundations of Computer Science MFCS 2012}. 7464th ed. Německo: Lecture Notes in Computer Science, Springer-Verlag, 2012, p.~419-430. ISBN~978-3-642-32588-5. Available from: https://dx.doi.org/10.1007/978-3-642-32589-2\_{}38.
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