On Low Tree-Depth Decompositions

The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree-depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompos...

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Bibliographic Details
Published in:	Graphs and combinatorics Vol. 31; no. 6; pp. 1941 - 1963
Main Authors:	Nešetřil, Jaroslav, Ossona de Mendez, Patrice
Format:	Journal Article
Language:	English
Published:	Tokyo Springer Japan 01-11-2015
Subjects:	Combinatorics Engineering Design Mathematics Mathematics and Statistics Original Paper Classes with bounded expansion Graph decomposition 05C75 Nowhere dense classes 05C85 Model checking Low tree-depth decomposition 05C70 Homomorphism duality Tree-depth 05C15
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Summary:	The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree-depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompose and construct more complex graphs and structures. In more technical terms we survey some of the properties and applications of low tree-depth decomposition of graphs.
ISSN:	0911-0119 1435-5914
DOI:	10.1007/s00373-015-1569-7