The History of Degenerate (Bipartite) Extremal Graph Problems Page 1 BOLYAI SOCIETY
Erdos Centennial MATHEMATICAL STUDIES, 25 pp. 169–264. The History of Degenerate (Bipartite) …

Random graphs have proven to be one of the most important and fruitful concepts in modern
Combinatorics and Theoretical Computer Science. Besides being a fascinating study …

This survey is two-fold. We first report new progress on the spectral extremal results on the
Tur\'{a} n type problems in graph theory. More precisely, we shall summarize the spectral …

In this survey we consider extremal problems for cycles of prescribed lengths in graphs. The
general extremal problem is cast as follows: if 𝒞 C is a set of cycles, determine the largest …

The projective and polar geometries that arise from a vector space over a finite field are
particularly useful in the construction of combinatorial objects, such as latin squares …

Given a graph H and a set of graphs F, let ex (n, H, F) denote the maximum possible number
of copies of H in an F-free graph on n vertices. We investigate the function ex (n, H, F), when …

For fixed s 3, we prove that if optimal Ks-free pseudorandom graphs exist, then the Ramsey
number rs; t/is ts1Co. 1/as t! 1. Our method also improves the best lower bounds for rC; …

The paper is devoted to the study of a linguistic dynamical system of dimension n≥ 2 over
an arbitrary commutative ring K, ie, a family F of nonlinear polynomial maps f α: K n→ K n …

The Turán function $\mathrm {ex}(n, F) $ is the maximum number of edges in an $ F $-free
graph on $ n $ vertices. The question of estimating this function for $ F= C_ {2k} $, the cycle …

Let H 1, H 2,..., H k+ 1 be a sequence of k+ 1 finite, undirected, simple graphs. The
(multicolored) Ramsey number r (H 1, H 2,..., H k+ 1) is the minimum integer r such that in …