Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unavoidable chromatic patterns in 2-colorings of the complete graph   We consider unavoidable chromatic patterns in $2$-colorings of the edges of
the complete graph. Several such problems are explored being a junction point
between Ramsey theory, extremal graph theory (Tur\'an type problems), zero-sum
Ramsey theory, and interpolation theorems in graph theory. A role-model of
these problems is the following: Let $G$ be a graph with $e(G)$ edges. We say
that $G$ is omnitonal if there exists a function ${\rm ot}(n,G)$ such that the
following holds true for $n$ sufficiently large: For any $2$-coloring $f:
E(K_n) \to \{red, blue \}$ such that there are more than ${\rm ot}(n,G)$ edges
from each color, and for any pair of non-negative integers $r$ and $b$ with
$r+b = e(G)$, there is a copy of $G$ in $K_n$ with exactly $r$ red edges and
$b$ blue edges. We give a structural characterization of omnitonal graphs from
which we deduce that omnitonal graphs are, in particular, bipartite graphs, and
prove further that, for an omnitonal graph $G$, ${\rm ot}(n,G) =
\mathcal{O}(n^{2 - \frac{1}{m}})$, where $m = m(G)$ depends only on $G$. We
also present a class of graphs for which ${\rm ot}(n,G) = ex(n,G)$, the
celebrated Tur\'an numbers. Many more results and problems of similar flavor
are presented.

37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph