Given a graph G on k edges, we consider the following two extremal problems: provided n is
large enough, what is the minimum integer bal (n, G), if it exists, such that any 2‐coloring of …

We consider $2 $-colourings $ f: E (G)\rightarrow\{-1, 1\} $ of the edges of a graph $ G $ with
colours $-1$ and $1 $ in $\mathbb {Z} $. A subgraph $ H $ of $ G $ is said to be a zero-sum …

We study a Tur\'an-type problem on edge-colored complete graphs. We show that for any $ r
$ and $ t $, any sufficiently large $ r $-edge-colored complete graph on $ n $ vertices with …

Given a graph G, a 2-coloring of the edges of K n is said to contain a balanced copy of G if
we can find a copy of G such that half of its edges are in each color class. If, for every …

In Ramsey theory for graphs we are given a graph $ G $ and we are required to find the
least $ n_0 $ such that, for any $ n\geq n_0 $, any red/blue colouring of the edges of $ K_n …

We study the color patterns that, for $ n $ sufficiently large, are unavoidable in $2 $-colorings
of the edges of a complete graph $ K_n $ with respect to $\min\{e (R), e (B)\} $, where $ e (R) …

We study Turán‐and Ramsey‐type problems on edge‐colored graphs. A two‐edge‐colored
graph is called ε ε‐balanced if each color class contains at least an ε ε‐proportion of its …

An edge-colouring of a graph $ G $ is said to be colour-balanced if there are equally many
edges of each available colour. We are interested in finding a colour-balanced perfect …

One of the central goals in extremal combinatorics is to understand how the global structure
of a combinatorial object, eg a graph, hypergraph or set system, is affected by local …

In this paper, we study the existence of unavoidable 2-edge-colored patterns in edge-
colorings of the complete graph. We are interested in how these patterns change as the …