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 …

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 …

Fix a graph F and a positive integer r. With a graph G, we associate the quantity cr, F (G), the
number of r-colorings of the edge set of G with no monochromatic copy of F as a subgraph …

The Center for Interdisciplinary Research (ZiF) at the University of Bielefeld hosted a
cooperation group under the title “Search Methodologies”, from October 1, 2010 to …

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 …

For fixed positive integers r, k and ℓ with 1≤ ℓ< r and an r-uniform hypergraph H, let κ (H, k,
ℓ) denote the number of k-colorings of the set of hyperedges of H for which any two …

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 …

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 …

For a set of positive integers A⊆[n], an r-coloring of A is rainbow sum-free if it contains no
rainbow Schur triple. In this paper we initiate the study of the rainbow Erdős-Rothschild …