For positive integers 𝑛, 𝑟, 𝑠 with 𝑟> 𝑠, the set-coloring Ramsey number 𝑅 (𝑛; 𝑟, 𝑠) is the
minimum 𝑁 such that if every edge of the complete graph 𝐾 𝑁 receives a set of 𝑠 colors from …

We study edge-labelings of the complete bidirected graph K^↔ _n with functions that map
the set [d]={1,…, d} to itself. We call a directed cycle in K^↔ _n a fixed-point cycle if …

We study two related problems concerning the number of homogeneous subsets of given
size in graphs that go back to questions of Erdős. Most notably, we improve the upper …

Extending an earlier conjecture of Erdos, Burr and Rosta conjectured that among all two-
colorings of the edges of a complete graph, the uniformly random coloring asymptotically …

The set‐coloring Ramsey number R r, s (k) R _ r, s (k) is defined to be the minimum nn such
that if each edge of the complete graph K n K _n is assigned a set of ss colors from 1,…, r\left …

The Erd\H {o} s-Gy\'arf\'as number $ f (n, p, q) $ is the smallest number of colors needed to
color the edges of the complete graph $ K_n $ so that all of its $ p $-clique spans at least $ q …

The $ r $-colour Ramsey number $ R_r (k) $ is the minimum $ n\in\mathbb {N} $ such that
every $ r $-colouring of the edges of the complete graph $ K_n $ on $ n $ vertices contains a …

Motivated by an extremal problem on graph-codes that links coding theory and graph theory,
Alon recently proposed a question aiming to find the smallest number $ t $ such that there is …

We study a generalization of a famous result of Goodman and establish that asymptotically
at least a $1/256$ fraction of all triangles needs to be monochromatic in any four-coloring of …

The study of ordered Ramsey numbers of monotone paths for graphs and hypergraphs has
a long history, going back to the celebrated work by Erdős and Szekeres in the early days of …