This comprehensive review provides an in-depth analysis of graph theory, various graph
types, and the role of graph visualization in scientific studies. Graphs serve as powerful tools …

Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

Discrepancy theory is also called the theory of irregularities of distribution. Here are some
typical questions: What is the" most uniform" way of dis tributing n points in the unit square …

This paper is the second part of a broader survey of computational convexity, an area of
mathematics that has crystallized around a variety of results, problems and applications …

We study connections between distributed local algorithms, finitary factors of iid processes,
and descriptive combinatorics in the context of regular trees. We extend the Borel …

We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …

The main topic of the book is amenable groups, ie, groups on which there exist invariant
finitely additive measures. It was discovered that the existence or non-existence of …

We study the local complexity landscape of locally checkable labeling (LCL) problems on
constant-degree graphs with a focus on complexities below log* n. Our contribution is …

We give a completely constructive solution to Tarski's circle squaring problem. More
generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If …

Take an apple and cut it into five pieces. Would you believe that these five pieces can be
reassembled in such a fashion so as to create two apples equal in shape and size to the …