Extremal Results for Random Discrete Structures

نویسنده

  • MATHIAS SCHACHT
چکیده

We study thresholds for extremal properties of random discrete structures. We determine the threshold for Szemerédi’s theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions and we determine the threshold for Turán-type problems for random graphs and hypergraphs. In particular, we verify a conjecture of Kohayakawa, Luczak, and Rödl for Turán-type problems in random graphs. Similar results were obtained by Conlon and Gowers.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Extremal Properties of Random Structures

The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety of unusual time dependences and system-size dependences for basic extremal properties are obtained.

متن کامل

Turánnical hypergraphs

This paper is motivated by the question of how global and dense restriction sets in results from extremal combinatorics can be replaced by less global and sparser ones. The result we consider here as an example is Turán’s theorem, which deals with graphs G = ([n], E) such that no member of the restriction set R = ` [n] r ́ induces a copy of Kr. Firstly, we examine what happens when this restrict...

متن کامل

Extremal Results in Random Graphs

According to Paul Erdős [Some notes on Turán’s mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Turán who “created the area of extremal problems in graph theory”. However, without a doubt, Paul Erdős popularized extremal combinatorics, by his many contributions to the field, his numerous questions and conjectures, and his influence on discrete mathematicians in Hungary and al...

متن کامل

Methods and Challenges in Extremal and Probabilistic Combinatorics∗ Organizers

Combinatorics, or discrete mathematics, is a fundamental mathematical discipline, concerned with the study of discrete mathematical objects such as graphs, set families and permutations, their typical and extremal properties, and their enumeration. A natural mathematical framework for a large variety of human activities and endeavors, combinatorics has been in existence for thousands of years. ...

متن کامل

Extremal properties of random mosaics

László Fejes Tóth’s fascinating book [2] demonstrates in many ways the phenomenon that figures of discrete or convex geometry that are very economical, namely solving an extremal problem of isoperimetric type, often show a high degree of symmetry. Among the examples are also planar mosaics where, for instance, an extremal property leads to the hexagonal pattern. Mosaics, or tessellations, have ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009