When Trees Grow Low: Shrubs and Fast MSO1
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Proceedings |
| Conference | Math Foundations of Computer Science MFCS 2012 |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-642-32589-2_38 |
| Field | Informatics |
| Keywords | tree-depth; shrub-depth; MSO model checking |
| 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 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. |
| Related projects: |