Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper Domination: towards a dichotomy through boundary properties   An upper dominating set in a graph is a minimal (with respect to set
inclusion) dominating set of maximum cardinality. The problem of finding an
upper dominating set is generally NP-hard. We study the complexity of this
problem in classes of graphs defined by finitely many forbidden induced
subgraphs and conjecture that the problem admits a dichotomy in this family,
i.e. it is either NP-hard or polynomial-time solvable for each class in the
family. A helpful tool to study the complexity of an algorithmic problem on
finitely defined classes of graphs is the notion of boundary classes. However,
none of such classes has been identified so far for the upper dominating set
problem. In the present paper, we discover the first boundary class for this
problem and prove the dichotomy for classes defined by a single forbidden
induced subgraph.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph