The ultimate interval graph recognition algorithm?
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On claw-free asteroidal triple-free graphs
Discrete Applied Mathematics
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the Power of BFS to Determine a Graphs Diameter
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Linear Time Algorithms for Hamiltonian Problems on (Claw, Net)-Free Graphs
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
On the Domination Search Number
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Recognizing Graphs without Asteroidal Triples
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
On the domination search number
Discrete Applied Mathematics
On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
Induced matchings in asteroidal triple-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Algorithms for graphs with small octopus
Discrete Applied Mathematics
Hereditary dominating pair graphs
Discrete Applied Mathematics
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Discrete Applied Mathematics
Discrete Applied Mathematics
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
On end-vertices of Lexicographic Breadth First Searches
Discrete Applied Mathematics
The LBFS Structure and Recognition of Interval Graphs
SIAM Journal on Discrete Mathematics
Separator orders in interval, cocomparability, and AT-free graphs
Discrete Applied Mathematics
Domination search on graphs with low dominating-target-number
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Roman domination over some graph classes
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Ultimate generalizations of LexBFS and LEX m
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Lexicographic breadth first search – a survey
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Collective tree spanners and routing in AT-free related graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Approximability of the path-distance-width for AT-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Induced disjoint paths in AT-Free graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Approximating the path-distance-width for AT-free graphs and graphs in related classes
Discrete Applied Mathematics
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An independent set of three vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triple. The motivation for this investigation is provided, in part, by the fact that AT-free graphs offer a common generalization of interval, permutation, trapezoid, and cocomparability graphs.Previously, the authors have given an existential proof of the fact that every connected AT-free graph contains a dominating pair, that is, a pair of vertices such that every path joining them is a dominating set in the graph. The main contribution of this paper is a constructive proof of the existence of dominating pairs in connected AT-free graphs. The resulting simple algorithm, based on the well-known lexicographic breadth-first search, can be implemented to run in time linear in the size of the input, whereas the best algorithm previously known for this problem has complexity O(|V|3) for input graph G=(V,E). In addition, we indicate how our algorithm can be extended to find, in time linear in the size of the input, all dominating pairs in a connected AT-free graph with diameter greater than 3. A remarkable feature of the extended algorithm is that, even though there may be O(|V|2) dominating pairs, the algorithm can compute and represent them in linear time.