We show that any 2-coloring of N contains infinitely many monochromatic sets of the form {x,
y, xy, x+ y}, and more generally monochromatic sets of the form {xi,∏ xi,∑ xi: i≤ n} for any …

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 …

This paper offers a systematic study of a family of graphs called amoebas. Amoebas recently
emerged from the study of forced patterns in $2 $-colorings of the edges of the complete …

We prove the following results solving a problem raised by Caro and Yuster (Graphs Comb
32: 49–63, 2016). For a positive integer m ≥ 2 m≥ 2, m ≠ 4 m≠ 4, there are infinitely many …

We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and by
Fox and Sudakov. First, for t≥ 3, we show that any two-colouring of the complete graph on n …

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 …

Given a graph GG, its Ramsey number r (G) r(G) is the minimum NN so that every two‐
coloring of E (KN) E(K_N) contains a monochromatic copy of G G. It was conjectured by …

Given graphs G and H, we say G→ r H if every r-colouring of the edges of G contains a
monochromatic copy of H. Let H [t] denote the t-blowup of H. The blowup Ramsey number B …

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) …