Intersection graphs of paths in a tree
Journal of Combinatorial Theory Series B
Theory of linear and integer programming
Theory of linear and integer programming
An almost linear-time algorithm for graph realization
Mathematics of Operations Research
A note on line digraphs and the directed max-cut problem
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
The underlying graph of a line digraph
Discrete Applied Mathematics - Special double volume: interconnection networks
The arborescence-realization problem
Discrete Applied Mathematics
Handbook of combinatorics (vol. 1)
Matroid optimization and algorithms
Handbook of combinatorics (vol. 1)
Graph classes: a survey
On some properties of DNA graphs
Discrete Applied Mathematics
Graphs and Hypergraphs
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A Directed Path Family is a family of subsets of some finite ground set whose members can be realized as arc sets of simple directed paths in some directed graph. In this paper we show that recognizing whether a given family is a Directed Path family is an NP-Complete problem, even when all members in the family have at most two elements. If instead of a family of subsets, we are given a collection of words from some finite alphabet, then deciding whether there exists a directed graph G such that each word in the language is the set of arcs of some path in G, is a polynomial-time solvable problem.