Tree-width and path-width of comparability graphs of interval orders

Garbe, R.

doi:10.1007/3-540-59071-4_35

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“…For some special classes of graphs, it has been shown that the treewidth can be computed in polynomial time, as e.g. cographs [9], circular-arc graphs [35], chordal bipartite graphs [23], permutation graphs [10], circle graphs [19], cocomparability graphs of bounded dimension [25], cointerval graphs [16] and dtrapezoid graphs [31]. The algorithm for d-trapezoid graphs assumes that a d-trapezoid intersection model is part of the input.…”

Section: Introductionmentioning

confidence: 99%

Treewidth and Minimum Fill-in on d-Trapezoid Graphs

Bodlaender

Kloks

Kratsch

et al. 2002

Graph Algorithms and Applications I

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We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time On d. We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an On twG d,1 time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid graph is part of the input. As a consequence, the minimum fill-in and the minimum interval graph completion as well as the treewidth and the pathwidth of a given trapezoid graph (or permutation graph) can be computed in time On 2 , even if no intersection model is part of the input.

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