Algorithmic aspects of the intersection and overlap numbers of a graph

Danny Hermelin, Romeo Rizzi, Stéphane Vialette

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


The intersection number of a graph G is the minimum size of a set S such that G is an intersection graph of some family of subsets F ⊆ 2 S. The overlap number of G is defined similarly, except that G is required to be an overlap graph of F. Computing the overlap number of a graph has been stated as an open problem in [B. Rosgen and L. Stewart, 2010, arXiv:1008.2170v2] and [D.W. Cranston, et al., J. Graph Theory., 2011]. In this paper we show two algorithmic aspects concerning both these graph invariants. On the one hand, we show that the corresponding optimization problems associated with these numbers are both APX-hard, where for the intersection number our results hold even for biconnected graphs of maximum degree 7, strengthening the previously known hardness result. On the other hand, we show that the recognition problem for any specific intersection graph class (e.g. interval, unit disc, . . . ) is easy when restricted to graphs with fixed intersection number.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783642352607
StatePublished - 1 Jan 2012
Externally publishedYes
Event23rd International Symposium on Algorithms and Computation, ISAAC 2012 - Taipei, Taiwan, Province of China
Duration: 19 Dec 201221 Dec 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7676 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Symposium on Algorithms and Computation, ISAAC 2012
Country/TerritoryTaiwan, Province of China

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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