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On restrictions of balanced 2-interval graphs

By Philippe Gambette and Stéphane Vialette

Abstract

International audienceThe 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, ..

Topics: 2-interval graphs, graph classes, line graphs, quasi-line graphs, claw-free graphs, circular interval graphs, proper circular-arc graphs, bioinformatics, scheduling, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM], [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM]
Publisher: HAL CCSD
Year: 2007
DOI identifier: 10.1007/978-3-540-74839-7_6
OAI identifier: oai:HAL:hal-00141338v2
Provided by: Hal-Diderot
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