Surveys in combinatorics 2019 / edited by Allan Lo (University of Birmingham) [and three others].
This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. This biennial conference is a well-established international event, with speakers from around the world. The volume provides...
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Full Text (via Cambridge) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY :
Cambridge University Press,
2019.
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| Series: | London Mathematical Society lecture note series ;
456. |
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Table of Contents:
- Cover; Series information; Title page; Copyright information; Contents; Preface; Clique-width for hereditary graph classes; 1 Introduction; 1.1 Width Parameters; 1.2 Motivation for Width Parameters; 1.3 Focus: Clique-Width; 1.4 Aims and Outline; 2 Preliminaries; 3 Clique-Width; 4 Results on Clique-Width for Hereditary Graph Classes; 4.1 Considering H-Free Graphs Contained in Some Hereditary Graph Class; 4.2 Forbidding A Small Number of Graphs; 4.3 Forbidding Small Induced Subgraphs; 4.4 Considering Hereditary Graph Classes Closed Under Complementation
- 4.5 Forbidding with Respect to Other Graph Containment Relations5 Algorithmic Consequences; 5.1 Meta-Theorems; 5.2 A General Strategy for Finding Algorithms; 5.3 Atoms; 5.4 Graph Colouring; 5.5 Graph Isomorphism; 6 Well-Quasi-Orderability; 6.1 Well-Quasi-Orderability Preserving Operations; 6.2 Results for Hereditary Graph Classes; 7 Variants of Clique-Width; 7.1 Linear Clique-Width; 7.2 Power-Bounded Clique-Width; Acknowledgements; References; Analytic representations of large graphs; 1 Introduction; 2 Preliminaries; 3 Dense graph limits; 4 Finite forcibility; 5 Sparse graph limits
- AcknowledgementReferences; Topological connectedness and independent sets in graphs; 1 Introduction; 1.1 A tale of two complexes; 1.2 Simplicial complexes and connectedness; 2 Finding an IT using topological connectedness; 3 Lower bounds on connectedness; 3.1 Tools for proving lower bounds; 3.2 Graph parameters; 4 Applications; 4.1 Hypergraph matching; 4.2 Hamilton cycle problems; 4.3 Colouring; 5 Remarks and open problems; 5.1 Beyond independent transversals; 5.2 Open problems; Acknowledgements; References; Expanders
- how to find them, and what to find in them; 1 Introduction
- 2 Definition(s) of an expander3 Basic properties of [alpha]-expanders; 4 Examples of [alpha]-expanders; 5 Expanders and separators; 6 Finding large expanding subgraphs; 7 Long paths and cycles; 7.1 DFS algorithm; 7.2 Long paths; 7.3 Long cycles; 7.4 Cycle lengths; 8 Minors in expanding graphs; 8.1 Large minors in expanding graphs; 8.2 Complete minors in expanding graphs; 8.3 Large minors in random graphs; References; Supersingular isogeny graphs in cryptography; 1 Introduction; 2 Preliminaries; 2.1 Definitions and Background on Elliptic Curves; 2.2 Supersingular isogeny graphs; 3 Applications
- 3.1 Charles-Goren-Lauter Cryptographic Hash Function3.2 Key Exchange ([DFJP14]); 3.3 Identification Protocols; 4 Endomorphism Rings of Supersingular Elliptic Curves; 5 Relationships between Hard Problems; 5.1 Endomorphism Rings and Path Finding; 5.2 Path Finding and Key Exchange; 6 Other Graphs and Related Problems; 6.1 LPS graphs; 6.2 Path Finding in LPS Graphs; 6.3 Relationship to Quantum Computation; 6.4 Relationship between LPS and Pizer Graphs; Acknowledgements; References; Delta-matroids for graph theorists; 1 Introduction; 2 What is a delta-matroid?; 2.1 A warm up; 2.2 The definition