Abstract
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 language | English |
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Pages (from-to) | 519-552 |
Number of pages | 34 |
Journal | Journal of Graph Algorithms and Applications |
Volume | 26 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- 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)