Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Algorithms for No-Rainbow Coloring and Phylogenetic Decisiveness   The input to the no-rainbow hypergraph coloring problem is a hypergraph $H$
where every hyperedge has $r$ nodes. The question is whether there exists an
$r$-coloring of the nodes of $H$ such that all $r$ colors are used and there is
no rainbow hyperedge -- i.e., no hyperedge uses all $r$ colors. The no-rainbow
hypergraph $r$-coloring problem is known to be NP-complete for $r \geq 3$. The
special case of $r=4$ is the complement of the phylogenetic decisiveness
problem. Here we present a deterministic algorithm that solves the no-rainbow
$r$-coloring problem in $O^*((r-1)^{(r-1)n/r})$ time and a randomized algorithm
that solves the problem in $O^*((\frac{r}{2})^n)$ time.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas