Journal of Combinatorial Theory Series B
Distance-hereditary graphs, Steiner trees, and connected domination
SIAM Journal on Computing
Discrete Applied Mathematics - Computational combinatiorics
Journal of Graph Theory
Weighted connected k-domination and weighted k-dominating clique in distance-hereditary graphs
Theoretical Computer Science
Compact-port routing models and applications to distance-hereditary graphs
Journal of Parallel and Distributed Computing
Efficient Parallel and Linear Time Sequential Split Decomposition (Extended Abstract)
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Journal of Discrete Algorithms
Solving some NP-complete problems using split decomposition
Discrete Applied Mathematics
Shunting of Passenger Train Units: An Integrated Approach
Transportation Science
Discrete Applied Mathematics
Dynamic distance hereditary graphs using split decomposition
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Treelike comparability graphs: characterization, recognition, and applications
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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In this paper, we study the class of distance-hereditary comparability graphs, that is, those graphs which admit a transitive orientation and are completely decomposable with respect to the split decomposition. We provide a characterization based on a restricted number of forbidden subgraphs. We also provide further characterizations and one of them, based on the split decomposition, is used to devise a recognizing algorithm working in linear time. Finally, we show how to build distance-hereditary comparability graphs.