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- Paul Hunter, Stephan Kreutzer
- SODA
- 2007

We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, κ-trees and cops and robber games and study their natural translations to digraphs. Weâ€¦ (More)

- Isolde Adler, Martin Grohe, Stephan Kreutzer
- SODA
- 2008

By Robertson and Seymour's graph minor theorem, every minor ideal can be characterised by a finite family of excluded minors. (A <i>minor ideal</i> is a class of graphs closed under taking minors.)â€¦ (More)

- Dietmar Berwanger, Anuj Dawar, Paul Hunter, Stephan Kreutzer, Jan ObdrzÃ¡lek
- J. Comb. Theory, Ser. B
- 2012

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm design. Treewidth can beâ€¦ (More)

- Dietmar Berwanger, Anuj Dawar, Paul Hunter, Stephan Kreutzer
- STACS
- 2006

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width isâ€¦ (More)

- Martin Grohe, Stephan Kreutzer, Sebastian Siebertz
- STOC
- 2014

Nowhere dense graph classes, introduced by Nešetřil and Ossona de Mendez [2010, 2011], form a large variety of classes of “sparse graphs” including the class of planar graphs,â€¦ (More)

We consider monotonicity problems for graph searching games. Variants of these games â€“ defined by the type of moves allowed for the players â€“ have been found to be closely connected to graphâ€¦ (More)

- Stephan Kreutzer, Anuj Dawar
- Electronic Colloquium on Computational Complexity
- 2009

We show that if C is a class of graphs which is nowhere dense then rst-order model-checking is xed-parameter tractable on C. As all graph classes which exclude a xed minor, or are of bounded localâ€¦ (More)

- Anuj Dawar, Martin Grohe, Stephan Kreutzer
- 22nd Annual IEEE Symposium on Logic in Computerâ€¦
- 2007

We introduce the concept of locally excluded minors. Graph classes locally excluding a minor are a common generalisation of the concept of excluded minor classes and of graph classes with boundedâ€¦ (More)

- Anuj Dawar, Erich GrÃ¤del, Stephan Kreutzer
- CSL
- 2001

We consider an extension of modal logic with an operator for constructing inflationary fixed points, just as the modal μ-calculus extends basic modal logic with an operator for least fixed points.â€¦ (More)

- Stephan Kreutzer
- IWPEC
- 2008

Algorithmic meta-theorems are general algorithmic results applying to a whole range of problems, rather than just to a single problem alone. They often have a logical and a structural component, thatâ€¦ (More)