A note on the Hamiltonian circuit problem on directed path graphs
Information Processing Letters
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
Paths in interval graphs and circular arc graphs
Discrete Mathematics
Polynomial Algorithms for Hamiltonian Cycle in Cocomparability Graphs
SIAM Journal on Computing
Hamiltonian circuits in chordal bipartite graphs
Discrete Mathematics
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On computing a longest path in a tree
Information Processing Letters
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Finding paths and cycles of superpolylogarithmic length
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Finding large cycles in Hamiltonian graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Linear structure of bipartite permutation graphs and the longest path problem
Information Processing Letters
Algorithms for long paths in graphs
Theoretical Computer Science
Finding Long Paths, Cycles and Circuits
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Longest Path Problems on Ptolemaic Graphs
IEICE - Transactions on Information and Systems
The Longest Path Problem Is Polynomial on Interval Graphs
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Simple geometrical intersection graphs
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
Efficient algorithms for the longest path problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A polynomial time algorithm for longest paths in biconvex graphs
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Computing and counting longest paths on circular-arc graphs in polynomial time
Discrete Applied Mathematics
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The longest path problem is the problem of finding a path of maximum length in a graph. As a generalization of the Hamiltonian path problem, it is NP-complete on general graphs and, in fact, on every class of graphs that the Hamiltonian path problem is NP-complete. Polynomial solutions for the longest path problem have recently been proposed for weighted trees, ptolemaic graphs, bipartite permutation graphs, interval graphs, and some small classes of graphs. Although the Hamiltonian path problem on cocomparability graphs was proved to be polynomial almost two decades ago [9], the complexity status of the longest path problem on cocomparability graphs has remained open until now; actually, the complexity status of the problem has remained open even on the smaller class of permutation graphs. In this paper, we present a polynomial-time algorithm for solving the longest path problem on the class of cocomparability graphs. Our result resolves the open question for the complexity of the problem on such graphs, and since cocomparability graphs form a superclass of both interval and permutation graphs, extends the polynomial solution of the longest path problem on interval graphs [18] and provides polynomial solution to the class of permutation graphs.