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A Journey Through Discrete Mathematics

Editors: Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin

DOI: 10.1007/978-3-319-44479-6

ISBN: 978-3-319-44478-9

Publisher: Springer International Publishing - Springer Journals

May 10, 2017

11 - 20 of 32 Chapters

LitStream

Chapter 11Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story

Blagojević, Pavle V. M.; Ziegler, Günter M.

Pages: 273 –341

[Bárány’s “topological Tverberg conjecture” from 1976 states that any continuous map of an N-simplex ΔN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 12One-Sided Epsilon-Approximants

Bukh, Boris; Nivasch, Gabriel

Pages: 343 –356

[Given a finite point set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$P...
LitStream

Chapter 13A Note on Induced Ramsey Numbers

Conlon, David; Dellamonica, Domingos; La Fleur, Steven; Rödl, Vojtěch; Schacht, Mathias

Pages: 357 –366

[The induced Ramsey number rind(F) of a k-uniform hypergraph F is the smallest natural number n for which there exists a k-uniform hypergraph G on n vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of F. We study this function, showing that rind(F) is...
LitStream

Chapter 14ARRIVAL: A Zero-Player Graph Game in NP ∩ coNP

Dohrau, Jérôme; Gärtner, Bernd; Kohler, Manuel; Matoušek, Jiří; Welzl, Emo

Pages: 367 –374

[Suppose that a train is running along a railway network, starting from a designated origin, with the goal of reaching a designated destination. The network, however, is of a special nature: every time the train traverses a switch, the switch will change its position immediately afterwards....
LitStream

Chapter 15Constant-Factor Approximation for TSP with Disks

Dumitrescu, Adrian; Tóth, Csaba D.

Pages: 375 –390

[We revisit the traveling salesman problem with neighborhoods (TSPN) and present the first constant-ratio approximation for disks in the plane: Given a set of n disks in the plane, a TSP tour whose length is at most O(1) times the optimal can be computed in time that is polynomial in n. Our...
LitStream

Chapter 16Transport-Entropy Inequalities and Curvature in Discrete-Space Markov Chains

Eldan, Ronen; Lee, James R.; Lehec, Joseph

Pages: 391 –406

[Let G=(Ω,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G =...
LitStream

Chapter 17Bounding Helly Numbers via Betti Numbers

Goaoc, Xavier; Paták, Pavel; Patáková, Zuzana; Tancer, Martin; Wagner, Uli

Pages: 407 –447

[We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers b and d there exists an integer h(b, d) such that the following holds. If ℱ\documentclass[12pt]{minimal} \usepackage{amsmath}...
LitStream

Chapter 18Ruled Surface Theory and Incidence Geometry

Guth, Larry

Pages: 449 –466

[We survey the applications of ruled surface theory in incidence geometry. We discuss some of the proofs and raise some open questions.]
LitStream

Chapter 19Approximating the k-Level in Three-Dimensional Plane Arrangements

Har-Peled, Sariel; Kaplan, Haim; Sharir, Micha

Pages: 467 –503

[Let H be a set of n non-vertical planes in three dimensions, and let r < n be a parameter. We give a construction that approximates the (n∕r)-level of the arrangement 𝒜(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
LitStream

Chapter 20Schrijver Graphs and Projective Quadrangulations

Kaiser, Tomáš; Stehlík, Matěj

Pages: 505 –526

[In a recent paper, Kaiser and Stehlík (J Combin Theory Ser B 113:1–17, 2015) have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the n-dimensional projective space ℙn\documentclass[12pt]{minimal} \usepackage{amsmath}...

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