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Asymptotic properties of random graphs

Zbigniew Palka — 1988

CONTENTS1. Introduction...........................................................................5 1.1. Purpose and scope..........................................................5 1.2. Probability-theoretic preliminaries....................................6 1.3. Graphs............................................................................11 1.4. Random graphs..............................................................132. Vertex-degrees....................................................................15 2.1....

On pendant vertices in random graphs

Zbigniew Palka — 1981

Colloquium Mathematicae

Isolated trees in a bichromatic random graph

Zbigniew Pałka — 1982

Colloquium Mathematicae

Review

Zbigniew Palka — 2005

Mathematica Applicanda

In-degree sequence in a general model of a random digraph

Zbigniew Palka; Monika Sperling — 2006

Discussiones Mathematicae Graph Theory

A general model of a random digraph D(n,P) is considered. Based on a precise estimate of the asymptotic behaviour of the distribution function of the binomial law, a problem of the distribution of extreme in-degrees of D(n,P) is discussed.

On a sphere of influence graph in a one-dimensional space

Zbigniew Palka; Monika Sperling — 2005

Discussiones Mathematicae Graph Theory

A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.

On the size of a maximal induced tree in a random graph

Michał Karoński; Zbigniew Palka — 1980

Mathematica Slovaca

Addendum and erratum to the paper "On the size of a maximal induced tree in a random graph"

Michał Karoński; Zbigniew Palka — 1981