On restrictions of balanced 2-interval graphs
Abstract
The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify the introduction of a hierarchy of subclasses of 2-interval graphs that generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and (x,x)-interval graphs. We provide instances that show that all the inclusions are strict. We extend the NP-completeness proof of recognizing 2-interval graphs to the recognition of balanced 2-interval graphs. Finally we give hints on the complexity of unit 2-interval graphs recognition, by studying relationships with other graph classes: proper circular-arc, quasi-line graphs, K_{1,5}-free graphs, ...
Cite
@article{arxiv.0704.1571,
title = {On restrictions of balanced 2-interval graphs},
author = {Philippe Gambette and Stéphane Vialette},
journal= {arXiv preprint arXiv:0704.1571},
year = {2008}
}