Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing graphs with limited resources   We discuss the amount of physical resources required to construct a given
graph, where vertices are added sequentially. We naturally identify information
-- distinct into instructions and memory -- and randomness as resources. Not
surprisingly, we show that, in this framework, threshold graphs are the
simplest possible graphs, since the construction of threshold graphs requires a
single bit of instructions for each vertex and no use of memory. Large
instructions without memory do not bring any advantage. With one bit of
instructions and one bit of memory for each vertex, we can construct a family
of perfect graphs that strictly includes threshold graphs. We consider the case
in which memory lasts for a single time step, and show that as well as the
standard threshold graphs, linear forests are also producible. We show further
that the number of random bits (with no memory or instructions) needed to
construct any graph is asymptotically the same as required for the
Erd\H{o}s-R\'enyi random graph. We also briefly consider constructing trees in
this scheme. The problem of defining a hierarchy of graphs in the proposed
framework is fully open.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys