On the Helly Property of Some Intersection Graphs

  • Tanilson D. Santos UFRJ / UFT
  • Jayme Szwarcfiter UFRJ
  • Uéverton S. Souza UFF
  • Claudson F. Bornstein UFRJ


An EPG graph G is an edge-intersection graph of paths on a grid. In this thesis, we analyze structural characterizations and complexity aspects regarding EPG graphs. Our main focus is on the class of B1-EPG graphs whose intersection model satisfies well-known the Helly property, called Helly-B1-EPG. We show that the problem of recognizing Helly-B1-EPG graphs is NP-complete. Besides, other intersection graph classes such as VPG, EPT, and VPT were also studied. We completely solve the problem of determining the Helly and strong Helly numbers of Bk-EPG graphs and Bk-VPG graphs for each non-negative integer k. Finally, we show that every Chordal B1-EPG graph is at the intersection of VPT and EPT.
Palavras-chave: Helly property, Intersection graphs, NP-completeness


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SANTOS, Tanilson D.; SZWARCFITER, Jayme; SOUZA, Uéverton S.; BORNSTEIN, Claudson F.. On the Helly Property of Some Intersection Graphs. In: CONCURSO DE TESES E DISSERTAÇÕES (CTD), 34. , 2021, Evento Online. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2021 . p. 19-24. ISSN 2763-8820. DOI: https://doi.org/10.5753/ctd.2021.15752.