Dominating the complements of bounded tolerance graphs and the complements of trapezoid graphs
Discrete Applied Mathematics
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Finding Hamiltonian circuits in quasi-adjoint graphs
Discrete Applied Mathematics
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
Jump number maximization for proper interval graphs and series-parallel graphs
Information Sciences: an International Journal
The longest path problem is polynomial on cocomparability graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Reduced-by-matching Graphs: Toward Simplifying Hamiltonian Circuit Problem
Fundamenta Informaticae
Computing and counting longest paths on circular-arc graphs in polynomial time
Discrete Applied Mathematics
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Finding a Hamiltonian cycle in a graph is one of the classical NP-complete problems. Complexity of the Hamiltonian problem in permutation graphs has been a well-known open problem. In this paper the authors settle the complexity of the Hamiltonian problem in the more general class of cocomparability graphs. It is shown that the Hamiltonian cycle existence problem for cocomparability graphs is in $P$. A polynomial time algorithm for constructing a Hamiltonian path and cycle is also presented. The approach is based on exploiting the relationship between the Hamiltonian problem in a cocomparability graph and the bump number problem in a partial order corresponding to the transitive orientation of its complementary graph.