Journal of Combinatorial Theory Series B
Hamiltonian circuits in chordal bipartite graphs
Discrete Mathematics
An approximation algorithm for finding a long path in Hamiltonian graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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
Finding a Path of Superlogarithmic Length
SIAM Journal on Computing
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
The Hamiltonian problem on distance-hereditary graphs
Discrete Applied Mathematics
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Laminar structure of ptolemaic graphs and its applications
ISAAC'05 Proceedings of the 16th 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
Laminar structure of ptolemaic graphs with applications
Discrete Applied Mathematics
The longest path problem is polynomial on cocomparability graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Computing and counting longest paths on circular-arc graphs in polynomial time
Discrete Applied Mathematics
| Hi-index | 0.00 |
Longest path problem is a problem for finding a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, there are few known graph classes such that the longest path problem can be solved efficiently. Polynomial time algorithms for finding a longest cycle and a longest path in a Ptolemaic graph are proposed. Ptolemaic graphs are the graphs that satisfy the Ptolemy inequality, and they are the intersection of chordal graphs and distance-hereditary graphs. The algorithms use the dynamic programming technique on a laminar structure of cliques, which is a recent characterization of Ptolemaic graphs.