Threshold order

A partial order on a finite set $P$ with the property that there is a weight function $w : P \rightarrow \mathbf{R}$ and a threshold $T$ such that $C$ is a chain (linearly ordered subset) if and only if $\sum_{x \in C} w(x) \le T$. The comparability graph of a threshold order is a threshold graph.

References

• Andreas Brandstädt, Van Bang Le; Jeremy P. Spinrad, "Graph classes: a survey". SIAM Monographs on Discrete Mathematics and Applications 3. Society for Industrial and Applied Mathematics (1999) ISBN 978-0-898714-32-6 Zbl 0919.05001