Finite and Infinite Sets

Finite and Infinite Sets

Colloquia Mathematica Societatis János Bolyai, 37.

1st Edition - January 1, 1984

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  • Editors: A. Hajnal, L. Lovász, V. T. Sós
  • eBook ISBN: 9781483161228

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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

Product details

  • No. of pages: 438
  • Language: English
  • Copyright: © North Holland 1984
  • Published: January 1, 1984
  • Imprint: North Holland
  • eBook ISBN: 9781483161228

About the Editors

A. Hajnal

L. Lovász

Affiliations and Expertise

Princeton University, Department of Computer Science, USA

V. T. Sós

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