Edge-intersection graphs of boundary-generated paths in a grid

Martin Charles Golumbic, Gila Morgenstern, Deepak Rajendraprasad

Research output: Contribution to journalArticlepeer-review


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 in the graph if and only if the corresponding paths share at least one edge of the grid. For two boundary points p and q on two adjacent boundaries of a rectangular grid G, we call the unique single-bend path connecting p and q in G using no other boundary point of G as the path generated by (p,q). A path in G is called boundary-generated, if it is generated by some pair of points on two adjacent boundaries of G. In this article, we study the edge-intersection graphs of boundary-generated paths on a grid or ∂EPG graphs. The motivation for studying these graphs comes from problems in the context of circuit layout. We show that ∂EPG graphs can be covered by two collections of vertex-disjoint co-bipartite chain graphs. This leads us to a linear-time testable characterization of ∂EPG trees and also an almost tight upper bound on the equivalence covering number of general ∂EPG graphs. We also study the cases of two-sided ∂EPG and three-sided ∂EPG graphs, which are respectively, the subclasses of ∂EPG graphs obtained when all the boundary-vertex pairs which generate the paths are restricted to lie on at most two or three boundaries of the grid. For the former case, we give a complete characterization.

Original languageEnglish
Pages (from-to)214-222
Number of pages9
JournalDiscrete Applied Mathematics
StatePublished - 19 Feb 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.


  • B1-EPG graphs
  • Boundary-generated paths
  • Equivalence covering number
  • Linear k-arboricity

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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