Linear algorithm for optimal path cover problem on interval graphs
Information Processing Letters
Paths in interval graphs and circular arc graphs
Discrete Mathematics
Optimal path cover problem on block graphs and bipartite permutation graphs
Theoretical Computer Science
Hamiltonian circuits in chordal bipartite graphs
Discrete Mathematics
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A time-optimal solution for the path cover problem on cographs
Theoretical Computer Science
Parallel algorithms for Hamiltonian problems on quasi-threshold graphs
Journal of Parallel and Distributed Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Journal of Parallel and Distributed Computing
Node-Disjoint Paths Algorithm in a Transposition Graph
IEICE - Transactions on Information and Systems
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
An optimal parallel solution for the path cover problem on P4-sparse graphs
Journal of Parallel and Distributed Computing
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
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In this paper we study a generalization of the path cover problem, namely, the 2-terminal-set path cover problem, or 2TPC for short. Given a graph Gand two disjoint subsets $\mathcal{T}^1$ and $\mathcal{T}^2$ of V(G), a 2-terminal-set path cover of Gwith respect to $\mathcal{T}^1$ and $\mathcal{T}^2$ is a set of vertex-disjoint paths $\mathcal{P}$ that covers the vertices of Gsuch that the vertices of $\mathcal{T}^1$ and $\mathcal{T}^2$ are all endpoints of the paths in $\mathcal{P}$ and all the paths with both endpoints in $\mathcal{T}^1 \cup \mathcal{T}^2$ have one endpoint in $\mathcal{T}^1$ and the other in $\mathcal{T}^2$. The 2TPC problem is to find a 2-terminal-set path cover of Gof minimum cardinality; note that, if $\mathcal{T}^1 \cup \mathcal{T}^2$ is empty, the stated problem coincides with the classical path cover problem. The 2TPC problem generalizes some path cover related problems, such as the 1HP and 2HP problems, which have been proved to be NP-complete even for small classes of graphs. We show that the 2TPC problem can be solved in linear time on the class of cographs. The proposed linear-time algorithm is simple, requires linear space, and also enables us to solve the 1HP and 2HP problems on cographs within the same time and space complexity.