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When Trees Grow Low: Shrubs and Fast MSO1

Název česky Když stromy nízké: Keře a rychlá MSO1
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GANIAN Robert HLINĚNÝ Petr OBDRŽÁLEK Jan NEŠETŘIL Jaroslav OSSONA DE MENDEZ Patrice RAMADURAI Reshma

Druh Článek ve sborníku
Konference Math Foundations of Computer Science MFCS 2012
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1007/978-3-642-32589-2_38
Obor Informatika
Klíčová slova tree-depth; shrub-depth; MSO model checking
Popis 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.
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