Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More results on greedy defining sets   The greedy defining sets of graphs were appeared first time in [M. Zaker,
Greedy defining sets of graphs, Australas. J. Combin, 2001]. We show that to
determine the greedy defining number of bipartite graphs is an NP-complete
problem. This result answers affirmatively the problem mentioned in the
previous paper. It is also shown that this number for forests can be determined
in polynomial time. Then we present a method for obtaining greedy defining sets
in Latin squares and using this method, show that any $n\times n$ Latin square
has a GDS of size at most $n^2-(n\log n)/4$. Finally we present an application
of greedy defining sets in designing practical secret sharing schemes.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ