A conjecture of Erdős, Gyárfás, and Pyber says that in any edge-colouring of a complete
graph with r colours, it is possible to cover all the vertices with r vertex-disjoint …

We prove that every graph G has a vertex partition into a cycle and an anticycle (a cycle in
the complement of G). Emptyset, singletons and edges are considered as cycles. This …

This survey is devoted to problems and results concerning covering the vertices of edge
colored graphs or hypergraphs with monochromatic paths, cycles and other objects. It is an …

A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened
form) that, for every natural number Δ, there is a constant r Δ such that, for any connected n …

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 …

Erd\H {o} s, Gy\'arf\'as, and Pyber (1991) conjectured that every $ r $-colored complete graph
can be partitioned into at most $ r-1$ monochromatic components; this is a strengthening of …

We show in this paper that in every $3 $-coloring of the edges of $ K^ n $ all but $ o (n) $ of
its vertices can be partitioned into three monochromatic cycles. From this, using our earlier …

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 …

Lehel conjectured that in every 2-coloring of the edges of K n, there is a vertex disjoint red
and blue cycle which span V (K n). Łuczak, Rödl, and Szemerédi proved Lehel's conjecture …

Monochromatic path and cycle partitions in hypergraphs Page 1 Monochromatic path and cycle
partitions in hypergraphs ∗ András Gyárfás Alfréd Rényi Institute of Mathematics Hungarian …