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dvorak z graph minors theory applications 2025

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Textbook in PDF format Preface References Declarations Introduction Notation Minors: Definitions and Basic Results References Understanding the Structure Theorem Tree Decompositions and Treewidth The Basic Concepts Statement of the Minor Structure Theorem Treewidth Balanced Separators and Unbreakable Sets Tangles Brambles Grid Minors and Walls Which Obstruction Is the Best One? Operations on Tangles, Rank, and Freedom Pregrids Cleaning Up Path Systems Building the Base Constructing the Grid Erdős–Pósa for Planar Minors Treewidth in Graphs on Surfaces Respectful Tangles Slopes Pretangles and Slopes Tangles and Slopes Branch Decompositions and Related Parameters Pathwidth References References Linkedness Exploiting a Clique Minor Linkedness in Graphs of High Connectivity Unique Linkage Theorem Linked Tree Decompositions References Graphs on Surfaces Linkage Across a Disk or Cylinder Metric from Respectful Tangles The Definition of the Metric The Structure of Balls Clearing a Zone Linking Through a Cylindrical Grid Linking Across a Surface Constructions of Minors References Disjoint Crossed Paths Flat Wall Theorem Testing the Presence of a Minor Structure Around a Crossing Local Form of the Minor Structure Theorem Arranging a Graph on a Surface Finishing the Proof References Pointers and Sources Sources References Using the Structure Theorem Low-Treewidth Colorings Treewidth-Fragility of Minor-Closed Classes Applications of Treewidth-Fragility Approximation of the Chromatic Number Degeneracy-Treewidth Partitioning References Linear-Sized Grid Minors Linear-Sized Grid Contractions References Topological Minors Untangling the Cuts Structure in Minor-Free Graphs Dealing with a Clique Minor Local to Global References Minors in Large Connected Graphs Localizing Apices Taming Vortices From Vortical Decompositions to Strong Vortical Decompositions Guardrails Around a Vortex Enlarging a Vortex Establishing a Linkage Improved Structure Theorem Finding Large Bipartite Minors Coloring Kt-Minor-Free Graphs References Sources References Avoiding the Structure Theorem References Sublinear Separators Existence of Small Separators Applications References Chordal Partitions Fractional Chromatic Number Degeneracy and Its Generalizations References Chromatic Number Density Beyond the Density Relaxed Colorings References Product Structure Product Structure in Graphs on Surfaces Beyond Embedded Graphs Applications References Iterated BFS Layerings Baker-amenable Classes References Isomorphism Testing Weisfeiler-Lehman Algorithm Small Cuts from Stable Colorings Handling the Small Cuts Group Theoretic Ingredients Isomorphism Testing References References Name Index Index

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dvorak z graph minors theory applications 2025

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