Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid

Eranda   Çela , Elisabeth Gaar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In a representation of a graph G as an edge intersection graph of paths on a grid (EPG) every vertex of G is represented by a path on a grid and two paths share a grid edge iff the corresponding vertices are adjacent. In a monotonic EPG representation every path on the grid is ascending in both rows and columns. In a (monotonic) Bk-EPG representation every path on the grid has at most k bends. The (monotonic) bend number b(G) (bm(G)) of a graph G is the smallest natural number k for which there exists a (monotonic) Bk-EPG representation of G. In this paper we deal with the monotonic bend number of outerplanar graphs and show that bm(G)⩽2 holds for every outerplanar graph G. Moreover, we characterize the maximal outerplanar graphs and the cacti with (monotonic) bend number equal to 0, 1 and 2 in terms of forbidden induced subgraphs. As a byproduct we obtain low-degree polynomial time algorithms to construct (monotonic) EPG representations with the smallest possible number of bends for maximal outerplanar graphs and cacti.
Original languageEnglish
Pages (from-to) 519-552
Number of pages34
JournalJournal of Graph Algorithms and Applications
Issue number4
Publication statusPublished - 2022


  • cacti
  • intersection graphs
  • outerplanar graphs
  • paths on a grid

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science
  • Geometry and Topology
  • Computer Science(all)
  • Computer Science Applications
  • Computational Theory and Mathematics

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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