The Roberts characterization of proper and unit interval graphs

In this note, a constructive proof is given that the classes of proper interval graphs and unit interval graphs coincide, a result originally established by Fred S. Roberts. Additionally, the proof yields a linear-time and space algorithm to compute a unit interval representation, given a proper interval graph as input. Key words: proper interval graph, unit interval graph, constructive proof, efficient representation

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Frédéric Gardi
• Keywords: DM 2007, Interval Graph, Proper Interval Graph, Unit Interval Graph