Given a graph F and an integer r≥ 2, a partition F ̂ of the edge set of F into at most r
classes, and a graph G, define cr, F ̂ (G) as the number of r-colorings of the edges of G that …

Let k:=(k1,..., ks) be a sequence of natural numbers. For a graph G, let F (G; k) denote the
number of colourings of the edges of G with colours 1,..., s such that, for every c∈{1,..., s}, the …

We consider a multicolored version of a question posed by Erdös and Rothschild. For a
fixed positive integer r and a fixed graph F, we look for n-vertex graphs that admit the …

Inspired by previous work of Balogh (2006), we show that, given r≥ 5 and n large, the
balanced complete bipartite graph K n∕ 2, n∕ 2 is the n-vertex graph that admits the largest …

We consider an extremal problem motivated by a question of Erdős and Rothschild (Erdős,
1974) regarding edge-colorings of graphs avoiding a given monochromatic subgraph. An …

Given integers r≥ 2, k≥ 3 and 2≤ s≤(k 2), and a graph G, we consider r-edge-colorings of
G with no copy of a complete graph K k on k vertices where s or more colors appear, which …

We consider a version of the Erdős–Rothschild problem for families of graph patterns. For
any fixed k≥ 3, let r 0 (k) be the largest integer such that the following holds for all 2≤ r≤ r 0 …

The typical extremal problem asks how large a structure can be without containing a
forbidden substructure. The Erdős–Rothschild problem, introduced in 1974 by Erdős and …

A rainbow Erdős-Rothschild problem Page 1 A rainbow Erdos-Rothschild problem Carlos
Hoppena,1,2 Hanno Lefmannb,1,3 Knut Odermannb,1,4 a Instituto de Matemática …

Given a sequence of natural numbers and a graph G, let denote the number of colourings of
the edges of G with colours, such that, for every, the edges of colour c contain no clique of …