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Horizons of Combinatorics

Part of the Bolyai Society Mathematical Studies Book Series (volume 17)

Editors: Győri, Ervin; Katona, Gyula O. H.; Lovász, László; Sági, Gábor

DOI: 10.1007/978-3-540-77200-2

ISBN: 978-3-540-77199-9

Publisher: Springer Berlin Heidelberg - Springer Journals

Jan 1, 2008

1 - 10 of 13 Chapters

Available

Ballot Theorems, Old and New

Addario-Berry, L.; Reed, B. A.

Pages: 9 –35

[We begin by sketching the development of the classical ballot theorem as it first appeared in the Comptes Rendus de 1’Academie des Sciences. The statement that is fairly called the first Ballot Theorem was due to Bertrand: Theorem 1 ([8]). We suppose that two candidates have been submitted to a...
Available

Statistical Inference on Random Structures

Csiszár, Villő; Rejtő, Lídia; Tusnády, Gábor

Pages: 37 –66

[Randomness for a statistician must have some structure. In traditional combinatorics the word random means uniform distribution on a set which may be the set of all graphs with n vertices, the set of all permutations of the numbers N = (1,2,..., n), the set of all partitions of N, or any other...
Available

Proof Techniques for Factor Theorems

Egawa, Yoshimi

Pages: 67 –78

[In this paper, we consider only finite, undirected, simple graphs with no loops and no multiple edges. The purpose of this paper is to illustrate three different types of proof techniques for theorems concerning the existence of a 2-factor.]
Available

Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects

Fox, Jacob; Pach, János

Pages: 79 –103

[In their seminal paper [21], Erdős and Hajnal raised the following question. Is it true that for any graph G there exists a constant c = c(G) > 0 with the property that every graph of n vertices that contains no induced subgraph isomorphic to G has a complete or an empty induced subgraph of size...
Available

Old and New Problems and Results in Ramsey Theory

Graham, Ron

Pages: 105 –118

[In this note, I will describe a variety of problems from Ramsey theory on which I would like to see progress made. I will also discuss several recent results which do indeed make progress on some of these problems.]
Available

Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method)

Katona, Gyula O. H.

Pages: 119 –140

[Let [n] = 1,2,..., n be a finite set, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

Subsums of a Finite Sum and Extremal Sets of Vertices of the Hypercube

Miklós, Dezső

Pages: 141 –161

[We will investigate the maximum size of the subsets of the vertices of a hypercube satisfying the property that the subspace (or cone) spanned by them will not intersect (contain) a given — other — subset of the vertices of the cube. It will turn out that the two cases when, on one side, we...
Available

Combinatorial Conditions for the Rigidity of Tensegrity Frameworks

Recski, András

Pages: 163 –177

[Rigidity of bar-and-joint frameworks has been studied for centuries. If the exact positions of the joints of such a framework are known, the rank of the so called rigidity matrix determines whether the framework is rigid1. If the underlying graph is given only, the rigidity of the framework...
Available

Polygonal Graphs

Seress, Ákos

Pages: 179 –188

[A near-polygonal graph is a graph г with a distinguished set C of cycles of common length m such that each path of length two lies in a unique element of C. If m is the girth of г then the graph is called polygonal. We describe various constructions of polygonal and near-polygonal graphs, and...
Available

Infinite Combinatorics: From Finite to Infinite

Soukup, Lajos

Pages: 189 –213

[We investigate the relationship between some theorems in finite combinatorics and their infinite counterparts: given a “finite” result how one can get an “infinite” version of it? We will also analyze the relationship between the proofs of a “finite” theorem and the proof of its “infinite”...

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