Hamiltonian circuits in interval graph generalizations
Information Processing Letters
An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
The Hamiltonian circuit problem for circle graphs in NP-complete
Information Processing Letters
Paths in interval graphs and circular arc graphs
Discrete Mathematics
Longest cycles in threshold graphs
Discrete Mathematics
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Hamiltonian circuits in chordal bipartite graphs
Discrete Mathematics
Graph classes: a survey
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
An approximation algorithm for finding a long path in Hamiltonian graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Discrete Applied Mathematics
Journal of Computer and System Sciences
Parameterized Complexity
Linear structure of bipartite permutation graphs and the longest path problem
Information Processing Letters
Computing Phylogenetic Diversity for Split Systems
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Longest Path Problems on Ptolemaic Graphs
IEICE - Transactions on Information and Systems
The longest path problem is polynomial on cocomparability graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A polynomial time algorithm for longest paths in biconvex graphs
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Laminar structure of ptolemaic graphs and its applications
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Hardness of approximation and integer programming frameworks for searching for caterpillar trees
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Hardness of approximation and integer programming frameworks for searching for caterpillar trees
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Computing and counting longest paths on circular-arc graphs in polynomial time
Discrete Applied Mathematics
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The longest path problem is to find a longest path in a given graph While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, very few graph classes are known where the longest path problem can be solved efficiently For a tree, a simple linear time algorithm for the longest path problem is known We first generalize the algorithm, and it then solves the longest path problem efficiently for weighted trees, block graphs, ptolemaic graphs, and cacti We next propose three new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on those classes As a corollary, it is also shown that the problem can be solved efficiently on threshold graphs.