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

Eranda Cela, Elisabeth Gaar

Research output: Working paperDiscussion paper


n 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
Number of pages58
Publication statusPublished - 6 Aug 2019

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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