Fast generation of planar graphs. The program Plantri is described. Its principles of operation, the basis for its efficiency and the recursive algorithms behind many of its capabilities are shown. Plantri is the fastest isomorphism-free generator of many classes of planar graphs, including triangulations, quadrangulations and convex polytopes. Many applications in the natural sciences as well as in mathematics are presented. In addition, many counts of isomorphism classes of planar graphs compiled using Plantri are given. These include triangulations, quadrangulations, convex polytopes, several classes of cubic and quartic graphs and triangulations of disks.

References in zbMATH (referenced in 60 articles )

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  1. Goedgebeur, Jan; Meersman, Barbara; Zamfirescu, Carol T.: Graphs with few Hamiltonian cycles (2020)
  2. Klocker, Benedikt; Fleischner, Herbert; Raidl, Günther R.: A lower bound for the smallest uniquely Hamiltonian planar graph with minimum degree three (2020)
  3. Montejano, Luis; Pauli, Eric; Raggi, Miguel; Roldán-Pensado, Edgardo: The graphs behind reuleaux polyhedra (2020)
  4. Abrishami, Gholamreza; Rahbarnia, Freydoon: A note on the smallest connected non-traceable cubic bipartite planar graph (2019)
  5. Brinkmann, Gunnar; Ozeki, Kenta; Van Cleemput, Nico: Types of triangle in Hamiltonian triangulations and an application to domination and (k)-walks (2019)
  6. Brinkmann, G.; Zamfirescu, C. T.: Polyhedra with few 3-cuts are Hamiltonian (2019)
  7. Pivotto, Irene; Royle, Gordon: Highly-connected planar cubic graphs with few or many Hamilton cycles (2019)
  8. Dowden, Chris; Kang, Mihyun; Sprüssel, Philipp: The evolution of random graphs on surfaces (2018)
  9. Erokhovets, Nikolai: Construction of fullerenes and Pogorelov polytopes with 5-, 6- and one 7-gonal face (2018)
  10. Kang, Mihyun; Sprüssel, Philipp: Symmetries of unlabelled planar triangulations (2018)
  11. Tilley, James: Kempe-locking configurations (2018)
  12. Tuzun, Robert E.; Sikora, Adam S.: Verification of the Jones unknot conjecture up to 22 crossings (2018)
  13. Van Cleemput, Nicolas; Zamfirescu, Carol T.: Regular non-Hamiltonian polyhedral graphs (2018)
  14. Dowden, Chris; Kang, Mihyun; Sprüssel, Philipp: The evolution of random graphs on surfaces (2017)
  15. Even-Zohar, Chaim: Models of random knots (2017)
  16. Goedgebeur, Jan; Zamfirescu, Carol T.: Improved bounds for hypo-Hamiltonian graphs (2017)
  17. McKay, Brendan D.: Hypohamiltonian planar cubic graphs with girth 5 (2017)
  18. Sulanke, Thom: Generating maps on surfaces (2017)
  19. Wimmer, Lienhard: Covering the sphere with equal circles (2017)
  20. Brinkmann, Gunnar; Souffriau, Jasper; van Cleemput, Nico: On the strongest form of a theorem of Whitney for Hamiltonian cycles in plane triangulations (2016)

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