When Trees Grow Low: Shrubs and Fast MSO1 [chapter]

Robert Ganian, Petr Hliněný, Jaroslav Nešetřil, Jan Obdržálek, Patrice Ossona de Mendez, Reshma Ramadurai
2012 Lecture Notes in Computer Science  
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
more » ... xtension of cographs and of graphs with bounded shrubdepth -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.
doi:10.1007/978-3-642-32589-2_38 fatcat:ngfzh2gylrdhlbqeqr5fzaci4i