Abstract
In this paper, we provide efficient algorithms for a number of closely related problems. They are: threshold number 2 on split graphs, Ferrers dimension 2, biorder dimension 2, interval dimension 2, and the trapezoid graph recognition problems. We show that all these problems can be reduced to the 2-chain subgraph cover problem in O(n2) time. By introducing a new algorithm to reduce a 2-chain subgraph cover problem to a partial order dimension 2 problem in O(n2) time, we find an O(n2) time algorithm to solve the 2-chain subgraph cover problem. As a consequence, all the previously mentioned problems can be solved in O(n2) time. No other algorithm known to the authors can solve any of these problems in the same time bound.
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