Abstract
In this paper, at first we describe a graph representing all the weak-order extensions of a partially ordered set and an algorithm generating them. Then we present a graph representing all of the minimal weak-order extensions of a partially ordered set, and implying a generation algorithm. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.
Supported by IFP Digitale Filter.
This work was supported by the PROCOPE Program
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© 1997 Springer-Verlag Berlin Heidelberg
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Bertet, K., Gustedt, J., Morvan, M. (1997). Weak-order extensions of an order. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024488
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DOI: https://doi.org/10.1007/BFb0024488
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