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Algorithmic Aspects of Comparability Graphs and Interval Graphs

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Graphs and Order

Part of the book series: NATO ASI Series ((ASIC,volume 147))

Abstract

Comparability graphs are undirected graphs that represent the comparability relation of partial orders. They constitute an important interface between graphs and partial orders both for theoretical investigations on their structural properties, and the development of efficient algorithmic methods for otherwise NP-hard combinatorial (optimization) problems on partial orders and their comparability graphs.

The first part of the paper gives a survey of this second aspect of comparability graphs. Topics dealt with are algorithmic methods and the necessary theoretical background for comparability graph recognition, for constructing all partial orders with the same comparability graphs, for decomposing comparability graphs and partial orders, for determining comparability invariants such as order dimension or jump number by decomposition, and for solving combinatorial optimization problems on comparability graphs.

The second part deals with the related class of interval graphs, which are exactly the incomparability graphs of interval orders. Again, we represent algorithmic methods for interval graph recognition and for solving combinatorial optimization problems on these graphs.

We then demonstrate in the third part how comparability graphs and interval graphs can be used for solving specific applied problems such as the seriation problem in archeology or certain scheduling problems over partially ordered sets.

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  1. Lehrstuhl für Informatik IV, Technical University of Aachen, 51 Aachen, West Germany

    Rolf H. Möhring

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  1. Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada

    Ivan Rival

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Möhring, R.H. (1985). Algorithmic Aspects of Comparability Graphs and Interval Graphs. In: Rival, I. (eds) Graphs and Order. NATO ASI Series, vol 147. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5315-4_2

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