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 …

For graphs G1, G2,..., Gr, the Ramsey number R (G1, G2,..., Gr) is the smallest positive
integer n such that if the edges of a complete graph Kn are partitioned into r disjoint color …

Improving a result of Erdős, Gyárfás and Pyber for large n we show that for every integer r⩾
2 there exists a constant n0= n0 (r) such that if n⩾ n0 and the edges of the complete graph …

The Ramsey number for a triple of long even cycles Page 1 Journal of Combinatorial Theory,
Series B 97 (2007) 584–596 www.elsevier.com/locate/jctb The Ramsey number for a triple of …

The‐color bipartite Ramsey number of a bipartite graph is the least integer for which every‐
edge‐colored complete bipartite graph contains a monochromatic copy of. The study of …

We develop a new framework to study minimum dd‐degree conditions in kk‐uniform
hypergraphs, which guarantee the existence of a tight Hamilton cycle. Our main theoretical …

We study properties of random subcomplexes of partitions returned by (a suitable form of)
the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these …

Denote by R (L, L, L) the minimum integer N such that any 3-coloring of the edges of the
complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and …

For a graph G, the k-colour Ramsey number R k (G) is the least integer N such that every k-
colouring of the edges of the complete graph KN contains a monochromatic copy of G. Let C …

We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic
paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the …