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arXiv · 1709.00313

A Simple Proof Characterizing Interval Orders with Interval Lengths between 1 and $k$

Simona Boyadzhiyska·Garth Isaak·Ann Trenk
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Abstract

A poset $P= (X, \prec)$ has an interval representation if each $x \in X$ can be assigned a real interval $I_x$ so that $x \prec y$ in $P$ if and only if $I_x$ lies completely to the left of $I_y$. Such orders are called \emph{interval orders}. Fishburn proved that for any positive integer $k$, an interval order has a representation in which all interval lengths are between $1$ and $k$ if and only if the order does not contain $\mathbf{(k+2)+1}$ as an induced poset. In this paper, we give a simple proof of this result using a digraph model.

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Simona Boyadzhiyska, Garth Isaak, Ann Trenk. 2017-09-01. A Simple Proof Characterizing Interval Orders with Interval Lengths between 1 and $k$. https://doi.org/10.2140/involve.2018.11.893

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