Open Access

The interval count of interval graphs and orders: a short survey

  • Márcia R. Cerioli1, 2,
  • Fabiano de S. Oliveira1Email author and
  • Jayme L. Szwarcfiter1, 2, 3
Journal of the Brazilian Computer Society201118:47

https://doi.org/10.1007/s13173-011-0047-1

Received: 4 October 2011

Accepted: 31 October 2011

Published: 26 November 2011

Abstract

The interval count problem determines the smallest number of interval lengths needed in order to represent an interval model of a given interval graph or interval order. Despite the large number of studies about interval graphs and interval orders, surprisingly only a few results on the interval count problem are known. In this work, we provide a short survey about the interval count and related problems. a graph and the number of its maximal cliques.

Keywords

Interval countInterval lengthsNumber of lengths