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Conference Papers Year : 2007

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, ...
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Dates and versions

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

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Philippe Gambette, Stéphane Vialette. On restrictions of balanced 2-interval graphs. 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG'07), ?, Jun 2007, Dornburg, Germany. pp.55-65, ⟨10.1007/978-3-540-74839-7_6⟩. ⟨hal-00141338v2⟩
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