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Preprints, Working Papers, ... Year : 2007

On restrictions of 2-interval graphs


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, ...
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Dates and versions

hal-00141338 , version 1 (12-04-2007)
hal-00141338 , version 2 (11-06-2007)



Philippe Gambette, Stéphane Vialette. On restrictions of 2-interval graphs. 2007. ⟨hal-00141338v1⟩


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