Hardness and approximation for L-EPG and B1-EPG graphs

Dror Epstein, Martin Charles Golumbic, Abhiruk Lahiri, Gila Morgenstern

Research output: Contribution to journalArticlepeer-review


The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. We consider the case of single-bend paths and its subclass of ⌞-shaped paths, namely, the classes known as B1-EPG and ⌞-EPG graphs, respectively. We show that fully-subdivided graphs are ⌞-EPG graphs, and later use this result in order to show that the following problems are APX-hard on ⌞-EPG graphs: MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, and MAXIMUM WEIGHTED INDEPENDENT SET, and also that MINIMUM DOMINATING SET is NP-complete on ⌞-EPG graphs. We also observe that MINIMUM COLORING is NP-complete already on ⌞-EPG, which follows from a proof for B1-EPG in Epstein et al. (2013). Finally, we provide efficient constant-factor-approximation algorithms for each of these problems on B1-EPG graphs.

Original languageEnglish
Pages (from-to)224-228
Number of pages5
JournalDiscrete Applied Mathematics
StatePublished - 15 Jul 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • B1-EPG graphs
  • Edge intersection graph
  • Fully-subdivided graphs
  • Paths on a grid
  • k-simplicial graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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