Patrice Ossona de Mendez's Books

Sparsity

Graphs, Structures, and Algorithms

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

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Sparsity

Graphs, Structures, and Algorithms

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.

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Page Count

472

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642278752

ISBN 13

9783642278754

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

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A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.

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Page Count

108

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470440652

ISBN 13

9781470440657

Sparsity

Graphs, Structures, and Algorithms

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

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Sparsity

Graphs, Structures, and Algorithms

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

472

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642278752

ISBN 13

9783642278754

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

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A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

By: Jaroslav Nešetřil,Patrice Ossona de Mendez

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

108

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470440652

ISBN 13

9781470440657

Book's by Patrice Ossona de Mendez

Sparsity

Sparsity

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

Sparsity

Sparsity

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

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