Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colorings of hypergraphs, perfect graphs, and associated primes of
  powers of monomial ideals   There is a natural one-to-one correspondence between squarefree monomial
ideals and finite simple hypergraphs via the cover ideal construction. Let H be
a finite simple hypergraph, and let J = J(H) be its cover ideal in a polynomial
ring R. We give an explicit description of all associated primes of R/J^s, for
any power J^s of J, in terms of the coloring properties of hypergraphs arising
from H. We also give an algebraic method for determining the chromatic number
of H, proving that it is equivalent to a monomial ideal membership problem
involving powers of J. Our work yields two new purely algebraic
characterizations of perfect graphs, independent of the Strong Perfect Graph
Theorem; the first characterization is in terms of the sets Ass(R/J^s), while
the second characterization is in terms of the saturated chain condition for
associated primes.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex