Hamiltonian circuits in interval graph generalizations
Information Processing Letters
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
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Simple linear time recognition of unit interval graphs
Information Processing Letters
Hamiltonian circuits in chordal bipartite graphs
Discrete Mathematics
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
A time-optimal solution for the path cover problem on cographs
Theoretical Computer Science
A linear time recognition algorithm for proper interval graphs
Information Processing Letters
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
Recognizing and representing proper interval graphs in parallel using merging and sorting
Discrete Applied Mathematics
Hi-index | 5.23 |
We study a variant of the path cover problem, namely, the k-fixed-endpoint path cover problem, or kPC for short. Given a graph G and a subset T of k vertices of V(G), a k-fixed-endpoint path cover of G with respect to T is a set of vertex-disjoint paths P that covers the vertices of G such that the k vertices of T are all endpoints of the paths in P. The kPC problem is to find a k-fixed-endpoint path cover of G of minimum cardinality; note that, if T is empty (or, equivalently, k=0), the stated problem coincides with the classical path cover problem. The kPC problem generalizes some path cover related problems, such as the 1HP and 2HP problems, which have been proved to be NP-complete. Note that the complexity status for both 1HP and 2HP problems on interval graphs remains an open question (Damaschke (1993) [9]). In this paper, we show that the kPC problem can be solved in linear time on the class of proper interval graphs, that is, in O(n+m) time on a proper interval graph on n vertices and m edges. The proposed algorithm is simple, requires linear space, and also enables us to solve the 1HP and 2HP problems on proper interval graphs within the same time and space complexity.