Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 5 (2018), 893-900.

A simple proof characterizing interval orders with interval lengths between 1 and $k$

Simona Boyadzhiyska, Garth Isaak, and Ann N. Trenk

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A poset P=(X,) has an interval representation if each xX can be assigned a real interval Ix so that xy in P if and only if Ix lies completely to the left of Iy. Such orders are called interval orders. Fishburn (1983, 1985) 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 (k+2)+1 as an induced poset. In this paper, we give a simple proof of this result using a digraph model.

Article information

Involve, Volume 11, Number 5 (2018), 893-900.

Received: 31 August 2017
Revised: 30 January 2018
Accepted: 5 February 2018
First available in Project Euclid: 12 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C62: Graph representations (geometric and intersection representations, etc.) For graph drawing, see also 68R10 06A99: None of the above, but in this section

interval order interval graph semiorder


Boyadzhiyska, Simona; Isaak, Garth; Trenk, Ann N. A simple proof characterizing interval orders with interval lengths between 1 and $k$. Involve 11 (2018), no. 5, 893--900. doi:10.2140/involve.2018.11.893.

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