Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational complexity of distance edge labeling   The problem of Distance Edge Labeling is a variant of Distance Vertex
Labeling (also known as $L_{2,1}$ labeling) that has been studied for more than
twenty years and has many applications, such as frequency assignment.
  The Distance Edge Labeling problem asks whether the edges of a given graph
can be labeled such that the labels of adjacent edges differ by at least two
and the labels of edges of distance two differ by at least one. Labels are
chosen from the set $\{0,1,\dots,\lambda\}$ for $\lambda$ fixed.
  We present a full classification of its computational complexity - a
dichotomy between the polynomially solvable cases and the remaining cases which
are NP-complete. We characterise graphs with $\lambda \le 4$ which leads to a
polynomial-time algorithm recognizing the class and we show NP-completeness for
$\lambda \ge 5$ by several reductions from Monotone Not All Equal 3-SAT.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin