On restrictions of balanced 2-interval graphs

Philippe Gambette 1, * Stéphane Vialette 2
* Corresponding author
2 Algorithmics
LRI - Laboratoire de Recherche en Informatique
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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Submitted on : Monday, June 11, 2007 - 2:32:48 PM
Last modification on : Monday, December 9, 2019 - 5:24:08 PM
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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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