LIPIcs.FSTTCS.2013.21.pdf
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Characterisations of Nowhere Dense Graphs (Invited Talk)
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2013-12-10
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Martin Grohe, Stephan Kreutzer, and Sebastian Siebertz. Characterisations of Nowhere Dense Graphs (Invited Talk). In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 21-40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.FSTTCS.2013.21
Abstract
Nowhere dense classes of graphs were introduced by Nesetril and Ossona de Mendez as a model for "sparsity" in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of graph classes generalising for example classes of graphs which exclude a fixed minor, have bounded degree or bounded local tree-width. In this paper we give a self-contained introduction to the concept of nowhere dense classes of graphs focussing on the various ways in which they can be characterised. We also briefly sketch algorithmic applications these characterisations have found in the literature.
Subject Classification
Keywords
- Graph Algorithms
- Algorithmic Graph Structure Theory
- Finite Model Theory
- Nowhere Dense Classes of Graphs
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