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Proper and Unit Trapezoid Orders and Graphs

✍ Scribed by Kenneth P. Bogart; Rolf H. Möhring; Stephen P. Ryan

Book ID: 110231574
Publisher: Springer Netherlands
Year: 1998
Tongue: English
Weight: 847 KB
Volume: 15
Category: Article
ISSN: 0167-8094
DOI: 10.1023/a:1006042122315

No coin nor oath required. For personal study only.

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We say any order ~ is a tolerance order on a set of vertices if we may assign to each vertex x an interval Ix of real numbers and a real number tx called a tolerance in such a way that x~,y if and only if the overlap of Ix and ly is less than the minimum of t~ and ty and the center of I~ is less tha

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We show that, if a tolerance graph is the complement of a comparability graph, it is a trapezoid graph, i.e., the complement of an order of interval dimension at most 2. As consequences we are able to give obstructions for the class of bounded tolerance graphs and to give an example of a graph that