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Recent Trends in Combinatorics

  • Book
  • © 2016

Overview

Editors:
  1. Andrew Beveridge

    1. Dept of Math, Statistics & Comp.Sc, Macalester College, St. Paul, USA

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  2. Jerrold R. Griggs

    1. Dept. of Mathematics, University of South Carolina, Columbia, USA

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  3. Leslie Hogben

    1. Dept. of Mathematics, Iowa State University, Ames, USA

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  4. Gregg Musiker

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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  5. Prasad Tetali

    1. School of Mathematics & Computer Sc, Georgia Institute of Technology, Atlanta, USA

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  • Contains many surveys of active research areas in combinatorics that include open problems
  • Contributions are from leading experts
  • State of the art results presented
  • Includes supplementary material: sn.pub/extras

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 159)

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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Extremal and Probabilistic Combinatorics

    1. Front Matter

      Pages 1-1
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    2. Problems related to graph indices in trees

      • László Székely, Stephan Wagner, Hua Wang
      Pages 3-30

    3. The edit distance in graphs: Methods, results, and generalizations

      • Ryan R. Martin
      Pages 31-62

    4. Repetitions in graphs and sequences

      • Maria Axenovich
      Pages 63-81

    5. Extremal problems for cycles in graphs

      • Jacques Verstraëte
      Pages 83-116

    6. A survey of Turán problems for expansions

      • Dhruv Mubayi, Jacques Verstraëte
      Pages 117-143

    7. Recent advances on Dirac-type problems for hypergraphs

      • Yi Zhao
      Pages 145-165

    8. Rainbow Hamilton cycles in random graphs and hypergraphs

      • Asaf Ferber, Michael Krivelevich
      Pages 167-189

    9. Further applications of the Container Method

      • József Balogh, Adam Zsolt Wagner
      Pages 191-213

    10. Independent transversals and hypergraph matchings - an elementary approach

      • Penny Haxell
      Pages 215-233

    11. Giant components in random graphs

      • Mihyun Kang
      Pages 235-256

    12. Infinite random graphs and properties of metrics

      • Anthony Bonato, Jeannette Janssen
      Pages 257-273

    13. Nordhaus-Gaddum problems for Colin de Verdière type parameters, variants of tree-width, and related parameters

      • Leslie Hogben
      Pages 275-294

    14. Algebraic aspects of the normalized Laplacian

      • Steve Butler
      Pages 295-315

    15. Progress on poset-free families of subsets

      • Jerrold R. Griggs, Wei-Tian Li
      Pages 317-338

    16. The mathematics of causal sets

      • Graham Brightwell, Malwina Luczak
      Pages 339-365

  3. Additive and Analytic Combinatorics

    1. Front Matter

      Pages 367-367
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    2. Lectures on approximate groups and Hilbert’s 5th problem

      • Emmanuel Breuillard
      Pages 369-404

    3. Character sums and arithmetic combinatorics

      • Mei-Chu Chang
      Pages 405-417
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About this book

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when  combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

Editors and Affiliations

  • Dept of Math, Statistics & Comp.Sc, Macalester College, St. Paul, USA

    Andrew Beveridge

  • Dept. of Mathematics, University of South Carolina, Columbia, USA

    Jerrold R. Griggs

  • Dept. of Mathematics, Iowa State University, Ames, USA

    Leslie Hogben

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Gregg Musiker

  • School of Mathematics & Computer Sc, Georgia Institute of Technology, Atlanta, USA

    Prasad Tetali

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