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Computational complexity of distance edge labeling
The problem of Distance Edge Labeling is a variant of Distance Vertex
Labeling (also known as 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 for 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 which leads to a
polynomial-time algorithm recognizing the class and we show NP-completeness for
by several reductions from Monotone Not All Equal 3-SAT.Comment: 21 pages, IWOCA 201