Trapezoid graphs and their coloring
Discrete Applied Mathematics
Domination on cocomparability graphs
SIAM Journal on Discrete Mathematics
On the 2-chain subgraph cover and related problems
Journal of Algorithms
Dominations in trapezoid graphs
Information Processing Letters
Steiner set and connected domination in trapezoid graphs
Information Processing Letters
Weighted domination of cocomparability graphs
Discrete Applied Mathematics
Graph classes: a survey
Connected domination and dominating clique in trapezoid graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Fast Algorithms for Independent Domination and Efficient Domination in Trapezoid Graphs
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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Given the trapezoid diagram, the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in O(m + n) time; the results is recently improved to be O(n) time by Kohler. For the (vertex) weighted case, finding the minimum weighted connected dominating set in trapezoid graphs can be solved in O(m + n log n) time. Here n(m) denotes the number of vertices (edges) of the trapezoid graph. In this paper, we show a different approach for finding the minimum cardinality connected dominating set in trapezoid graphs using O(n) time. For finding the minimum weighted connected dominating set, we show the problem can be effciently solved in O(n log log n) time.