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| HAL: hal-00141338, version 2 |
| arXiv: 0704.1571 |
| DOI: 10.1007/978-3-540-74839-7_6 |
| Detailed view |  Export this paper |
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| 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG'07), Dornburg : Allemagne (2007) |
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| Available versions: | v1 (2007-04-12) | v2 (2007-06-11) |
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| On restrictions of balanced 2-interval graphs |
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Philippe Gambette 1Stéphane Vialette 2 |
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| (2007-12-06) |
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| 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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| 1: | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| 2: | Laboratoire de Recherche en Informatique (LRI) |
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CNRS : UMR8623 – Université Paris XI - Paris Sud |
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| Algorithmics |
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| Subject | : | Computer Science/Discrete Mathematics Computer Science/Data Structures and Algorithms Computer Science/Bioinformatics Life Sciences/Quantitative Methods |
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| 2-interval graphs – graph classes – line graphs – quasi-line graphs – claw-free graphs – circular interval graphs – proper circular-arc graphs – bioinformatics – scheduling |
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| hal-00141338, version 2 | |
| http://hal-univ-mlv.archives-ouvertes.fr/hal-00141338 | |
| oai:hal-univ-mlv.archives-ouvertes.fr:hal-00141338 | |
| From: Algo Ligm | |
| Submitted on: Monday, 11 June 2007 14:32:48 | |
| Updated on: Monday, 4 February 2008 13:41:10 | |
