One of the earliest results in Combinatorics is Mantel's theorem from 1907 that the largest
triangle-free graph on a given vertex set is complete bipartite. However, a seemingly similar …

Many important theorems and conjectures in combinatorics, such as the theorem of
Szemerédi on arithmetic progressions and the Erdős–Stone Theorem in extremal graph …

Power forecast for each renewable power plant (RPP) in the renewable energy clusters is
essential. Though existing graph neural networks (GNN)-based models achieve satisfactory …

We show that for any sequence $ f:{\bf N}\to\{-1,+ 1\} $ taking values in $\{-1,+ 1\} $, the
discrepancy $$\sup_ {n, d\in {\bf N}}\left|\sum_ {j= 1}^ nf (jd)\right| $$ of $ f $ is infinite. This …

One of the most basic questions one can ask about a graph H is: how many H-free graphs
on n vertices are there? For non-bipartite H, the answer to this question has been well …

A hereditary property of graphs is a collection of graphs which is closed under taking
induced subgraphs. The speed of P is the function n↦| Pn|, where Pn denotes the graphs of …

Denote by fn (H) the number of (labeled) H-free graphs on a fixed vertex set of size n. Erdős
conjectured that, whenever H contains a cycle,, yet it is still open for every bipartite graph …

Two central topics of study in combinatorics are the so-called evolution of random graphs,
introduced by the seminal work of Erdős and Rényi, and the family of $ H $-free graphs, that …

Abstract According to Paul Erdős au][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 …

Abstract Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is
very fast developing, and in this long but relatively short survey we select some of those …