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 …

Szemerédi's Regularity Lemma is an important tool in discrete mathematics. It says that, in
some sense, all graphs can be approximated by random-looking graphs. Therefore the …

Although the theory of random graphs is one of the youngest branches of graph theory, in
importance it is second to none. It began with some sporadic papers of Erdős in the 1940s …

Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, in
some sense, all graphs can be approximated by random-looking graphs. Therefore the …

The regularity lemma of Szemerédi asserts that every graph can be partitioned in a certain
regular way. This result has numerous applications, but its known proof is not algorithmic …

We show that the game chromatic number of a planar graph is at most 33. More generally,
there exists a function f: ℕ→ ℕ so that for each n∈ ℕ, if a graph does not contain a …

Vertex Coverings by Monochromatic Cycles and Trees Page 1 JOURNAL OF
COMBINATORIAL THEORY, Series B 51, 9c-95 (1991) Vertex Coverings by Monochromatic …

What conditions ensure that a graph G contains some given spanning subgraph H? The
most famous examples of results of this kind are probably Dirac's theorem on Hamilton …

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 graph H and an integer r≥ 2, the induced r-size-Ramsey number of H is defined to be
the smallest integer m for which there exists a graph G with m edges with the following …