Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 143809, 7 pages
http://dx.doi.org/10.1155/2014/143809
Research Article

A Characterization of 2-Tree Proper Interval 3-Graphs

1Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
2Mathematics Department, Western Oregon University, Monmouth, OR 97361, USA

Received 30 September 2013; Revised 12 December 2013; Accepted 15 December 2013; Published 23 February 2014

Academic Editor: Hong J. Lai

Copyright © 2014 David E. Brown and Breeann M. Flesch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An interval p-graph is the intersection graph of a collection of intervals which have been colored with p different colors with edges corresponding to nonempty intersection of intervals from different color classes. We characterize the class of 2-trees which are interval 3-graphs via a list of three graphs and three infinite families of forbidden induced subgraphs.