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Finite and Infinite Sets - 1st Edition - ISBN: 9780444868930, 9781483161228

Finite and Infinite Sets

1st Edition

Colloquia Mathematica Societatis János Bolyai, 37.

Editors: A. Hajnal L. Lovász V. T. Sós
eBook ISBN: 9781483161228
Imprint: North Holland
Published Date: 1st January 1984
Page Count: 438
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Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.

Table of Contents

Volume I



Scientific Program

List of Participants

On the Essential Chains and Squares

Cellular Automata in Trees

On the Distribution of the Number of Interior Points

Almost Disjoint Families of Countable Sets

Inductive Classes of Cubic Graphs

An Application of Lovâsz Local Lemma: There Exist an Infinite 01-Sequence Containing no Near Identical Intervals

Induced Subgraphs

Inverse Extremal Digraph Problems

On the Sperner-Type Conditions

Minimal Decomposition of All Graphs with Equinumerous Vertices and Edges into Mutually Isomorphic Subgraphs

On Irregularities of Distribution

Some Theorems of the Nordhaus—Gaddum Class

A Restricted Version of Hales—Jewett's Theorem

Size Ramsey Numbers Involving Matchings

Selectivity of Hypergraphs

Generalized Polymatroids

Matroids from Crossing Families

Families of Finite Sets with Missing Intersections

Extending Functions from Subsets

An Erdõs—Ko-Rado Type Theorem

Strong Systems of Representatives

Graphs Associated with an Integral Domain and their Applications

Monochromatic Paths in Infinite Coloured Graphs

Two-Colorings of Simple Arrangements

On Dumpling-Eating Giants

On Circular Flows in Graphs

Longest Circuits in 3-Connected Graphs

Volume II

A Generalized MFMC-Property and Multicommodity Cut Problems

Finding Special Subdivisions of K4 in a Graph

On the Average Height of Monotonically Labelled Binary Trees

Dense Systems of Almost-Disjoint Sets

On Hadwiger Numbers of a Graph and its Complement

The Numbers of Odd-Cycle-Free Graphs

Oriented Matroids as Signed Geometries Real in Corank 2

Multitransversals in τ-Critical Hypergraphs

Nested Transversals

Some Problems in Vertex Symmetric Graphs

Edge-Coloring of Composite Regular Graphs

The Generalized Dichromatic Number of a Digraph

Amalgamation of Matroids Along Hypergraphs

Strongly Perfect Line Graphs and Total Graphs

Some Problems of Self-Dual Matroids

On Spatial Representations of Finite Graphs

On Unavoidable Subgraphs of Tournaments

On a Classification of Graphs with Respect to the Properties of Neighbourhood Graphs

On Two Concepts of Discrepancy in a Class of Combinatorial Games

Quasi-Residual Designs, Codes and Graphs

Some Coverings Derived from Finite Planes

For t≥3, Every t-dimensional; Partial Order can be Embedded in a t + 1 -Irreducible Partial Order

Some Results on Uniquely Colourable Graphs

The Method of Set-Pairs for Extremal Problems in Hypergraphs

Are m Given Elements Neighbouring?

Subdirect Irreducibility and Dimensions of Digraphs

On the Connection of the Frobenius Problem and the Knapsack Problem

Kruskal-Katona's Theorem in Generalized Complexes

Criticity with Respect to Properties and Operations in Graph Theory

On a Generalized Williamson Equation

Generalized Matchings and Generalized Hermite Polynomials

On Two Problems from Extremal Graph Theory


Solutions of Problems

On the Number of Subdivisions of the Unit Square

On the Subdivision of the Unit Square into Rectangles with Equal Area


No. of pages:
© North Holland 1984
1st January 1984
North Holland
eBook ISBN:

About the Editors

A. Hajnal

L. Lovász

Affiliations and Expertise

Princeton University, Department of Computer Science, USA

V. T. Sós

Ratings and Reviews