Hamiltonian circuits in interval graph generalizations
Information Processing Letters
An optimal algorithm for finding a maximum independent set of a circular-arc graph
SIAM Journal on Computing
On mapping processes to processors in distributed systems
International Journal of Parallel Programming
Stability in circular arc graphs
Journal of Algorithms
The Hamiltonian circuit problem for circle graphs in NP-complete
Information Processing Letters
Linear algorithm for optimal path cover problem on interval graphs
Information Processing Letters
Optimal covering of cacti by vertex-disjoint paths
Theoretical Computer Science
Linear time algorithms on circular-arc graphs
Information Processing Letters
An O(n2 log n) algorithm for the Hamiltonian cycle problem on circular-arc graphs
SIAM Journal on Computing
Paths in interval graphs and circular arc graphs
Discrete Mathematics
Optimal path cover problem on block graphs and bipartite permutation graphs
Theoretical Computer Science
An O(nlogn) algorithm for finding minimal path cover in circular-arc graphs
CSC '93 Proceedings of the 1993 ACM conference on Computer science
Polynomial Algorithms for Hamiltonian Cycle in Cocomparability Graphs
SIAM Journal on Computing
The path-partition problem in block graphs
Information Processing Letters
$O(M.N)$ Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs
SIAM Journal on Computing
An O(n2 algorithm for circular-arc graph recognition
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal path cover problem on block graphs
Theoretical Computer Science
Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization
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
Information Processing Letters
Efficient Algorithms for the Hamiltonian Problem on Distance-Hereditary Graphs
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
An NP-hard problem in bipartite graphs
ACM SIGACT News
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Hamiltonian laceability of bubble-sort graphs with edge faults
Information Sciences: an International Journal
Finding a minimum path cover of a distance-hereditary graph in polynomial time
Discrete Applied Mathematics
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A path cover of a graph G = (V, E) is a family of vertex-disjoint paths that covers all vertices in V. Given a graph G, the path cover problem is to find a path cover of minimum cardinality. This paper presents a simple O(n)-time approximation algorithm for the path cover problem on circular-arc graphs given a set of n arcs with endpoints sorted. The cardinality of the path cover found by the approximation algorithm is at most one more than the optimal one. By using the result, we reduce the path cover problem on circular-arc graphs to the Hamiltonian cycle and Hamiltonian path problems on the same class of graphs in O(n) time. Hence the complexity of the path cover problem on circular-arc graphs is the same as those of the Hamiltonian cycle and Hamiltonian path problems on circular-arc graphs.