Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic numbers of directed hypergraphs with no "bad" cycles   Imagine that you are handed a rule for determining whether a cycle in a
digraph is "good" or "bad", based on which edges of the cycle are traversed in
the forward direction and which edges are traversed in the backward direction.
Can you then construct a digraph which avoids having any "bad" cycles, but has
arbitrarily large chromatic number?
  We answer this question when the rule is described in terms of a finite state
machine. The proof relies on Nesetril and Rodl's structural Ramsey theory of
posets with a linear extension. As an application, we give a new proof of the
Loop Lemma of Barto, Kozik, and Niven in the special case of bounded width
algebras.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph