
The Longest (s, t)paths of Oshaped Supergrid Graphs
In this paper, we continue the study of the Hamiltonian and longest (s, ...
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Unpaired manytomany disjoint path cover of balanced hypercubes
The balanced hypercube BH_n, which is a variant of the hypercube, was pr...
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Combinatorial Conditions for Directed Collapsing
The purpose of this article is to study directed collapsibility of direc...
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Kidney exchange and endless paths: On the optimal use of an altruistic donor
We consider a wellstudied online random graph model for kidney exchange...
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Path matrix and path energy of graphs
Given a graph G, we associate a path matrix P whose (i, j) entry represe...
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On the parameterized complexity of the Minimum Path Cover problem in DAGs
A minimum path cover (MPC) of a directed acyclic graph (DAG) G = (V,E) i...
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Effectively Counting st Simple Paths in Directed Graphs
An important tool in analyzing complex social and information networks i...
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Computing Directed Steiner Path Covers
In this article we consider the Directed Steiner Path Cover problem on directed cographs. Given a directed graph G=(V,E) and a subset T of V of socalled terminal vertices, the problem is to find a minimum number of vertexdisjoint simple directed paths, which contain all terminal vertices and a minimum number of nonterminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute in linear time a minimum Steiner path cover for directed cographs. This leads to a linear time computation of an optimal directed Steiner path on directed cographs, if it exists. Since the Steiner path problem generalizes the Hamiltonian path problem, our results imply the first linear time algorithm for the directed Hamiltonian path problem on directed cographs. We also give binary integer programs for the (directed) Hamiltonian path problem, for the (directed) Steiner path problem, and for the (directed) Steiner path cover problem. These integer programs can be used to minimize changeover times in pickandplace machines used by companies in electronic industry.
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