Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge-Colored Graphs with Applications To Homogeneous Faults   In this paper, we use the concept of colored edge graphs to model homogeneous
faults in networks. We then use this model to study the minimum connectivity
(and design) requirements of networks for being robust against homogeneous
faults within certain thresholds. In particular, necessary and sufficient
conditions for most interesting cases are obtained. For example, we will study
the following cases: (1) the number of colors (or the number of non-homogeneous
network device types) is one more than the homogeneous fault threshold; (2)
there is only one homogeneous fault (i.e., only one color could fail); and (3)
the number of non-homogeneous network device types is less than five.

29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph