When Trees Grow Low: Shrubs and Fast MSO1

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126098" target="_blank" >RIV/00216208:11320/12:10126098 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-32589-2_38" target="_blank" >http://dx.doi.org/10.1007/978-3-642-32589-2_38</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-32589-2_38" target="_blank" >10.1007/978-3-642-32589-2_38</a>

Result language
angličtina
Original language name
When Trees Grow Low: Shrubs and Fast MSO1
Original language description
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 ofa 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 extensionof cographs and of graphs with bounded shrub-depth m-partite cographs (still of bounded clique-width), which are well quasi-ordered by the relation to be an induced subgraph and therefore allow polynomial time testing of hereditary properties.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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