Algorithmic aspects of the intersection and overlap numbers of a graph

Dan Hermelin, Romeo Rizzi, Stéphane Vialette

Research output: Contribution to journalConference articlepeer-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 GB
Pages (from-to)465-474
Number of pages10
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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