Given a graph H, the Ramsey number r (H) is the smallest natural number N such that any
two-colouring of the edges of KN contains a monochromatic copy of H. The existence of …

Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical
computer science will welcome the new edition of this book.”-MAA Reviews Maintaining a …

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) …

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 …

Abstract Let H s, t 1,…, tk be the graph with s triangles and k odd cycles of lengths t 1,…, tk≥
5 intersecting in exactly one common vertex. Recently, Hou et al.(2018)[27], and Yuan …

Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and
suppose that at least ε n2 edges have to be deleted from it to make it H-free. We show that in …

We describe a simple and yet surprisingly powerful probabilistic technique which shows
how to find in a dense graph a large subset of vertices in which all (or almost all) small …

For a fixed graph H, we define the rainbow Turán number ex∗(n, H) to be the maximum
number of edges in a graph on n vertices that has a proper edge-colouring with no rainbow …

The celebrated Kővári-Sós-Turán theorem states that any n-vertex graph containing no copy
of the complete bipartite graph K s, s has at most O s (n 2− 1/s) edges. In the past two …

The r-expansion G+ of a graph G is the r-uniform hypergraph obtained from G by enlarging
each edge of G with a vertex subset of size r− 2 disjoint from V (G) such that distinct edges …