| Description |
1 online resource (ix, 543 pages) |
| Series |
Lecture notes in logic ; 47
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Lecture notes in logic ; 47.
|
| Summary |
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Introduction -- Background from graph theory and logic -- Descriptive complexity -- Treelike decompositions -- Definable decompositions -- Graphs of bounded tree width -- Ordered treelike decompositions -- 3-connected components -- Graphs embeddable in a surface -- Quasi-4-connected components -- K5-minor-free graphs -- Completions of pre-decompositions -- Almost planar completions -- Almost-embeddable graphs -- Decompositions of almost-embeddable graphs -- Graphs with excluded minors -- Bits and pieces. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Graph theory.
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MATHEMATICS -- General. |
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Teoría de grafos |
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Matemáticas |
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Graph theory |
| Added Author |
Association for Symbolic Logic.
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| ISBN |
9781139028868 (electronic bk.) |
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1139028863 (electronic bk.) |
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9781108234702 (electronic bk.) |
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1108234704 (electronic bk.) |
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9781107014527 (hardcover) |
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1107014522 (hardcover) |
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