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 37 articles )

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  1. Sulanke, Thom: Generating maps on surfaces (2017)
  2. Wimmer, Lienhard: Covering the sphere with equal circles (2017)
  3. Cantarella, Jason; Chapman, Harrison; Mastin, Matt: Knot probabilities in random diagrams (2016)
  4. Ichihara, Kazuhiro; Masai, Hidetoshi: Exceptional surgeries on alternating knots (2016)
  5. Musin, Oleg R.; Nikitenko, Anton V.: Optimal packings of congruent circles on a square flat torus (2016)
  6. Zhu, Enqiang; Li, Zepeng; Shao, Zehui; Xu, Jin: Acyclically 4-colorable triangulations (2016)
  7. Cardinal, Jean; Hoffmann, Michael; Kusters, Vincent: On universal point sets for planar graphs (2015)
  8. Goedgebeur, Jan; McKay, Brendan D.: Recursive generation of IPR fullerenes (2015)
  9. Jablan, Slavik; Kauffman, Louis H.; Lopes, Pedro: The delunification process and minimal diagrams (2015)
  10. Matsumoto, Naoki; Nakamoto, Atsuhiro: Generating 4-connected even triangulations on the sphere (2015)
  11. Musin, O.R.; Tarasov, A.S.: Extremal problems of circle packings on a sphere and irreducible contact graphs (2015)
  12. Chen, Yaojun; Cheng, T.C.E.; Zhang, Yunqing; Zhou, Guofei: The planar Ramsey number $\mathrmPR(C_4,K_8)$ (2014)
  13. Grubman, Tony; Wanless, Ian M.: Growth rate of canonical and minimal group embeddings of spherical Latin trades (2014)
  14. Malestein, Justin; Rivin, Igor; Theran, Louis: Topological designs (2014)
  15. Musin, O.R.; Tarasov, A.S.: Enumeration of irreducible contact graphs on the sphere (2014)
  16. Wynn, Ed: Exhaustive generation of `Mrs. Perkins’s quilt’ square dissections for low orders (2014)
  17. Butler, Steve; Graham, Ron; Guettler, Gerhard; Mallows, Colin: An interstice relationship for flowers with four petals (2013)
  18. Choi, Suyoung: Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbers (2013)
  19. Flatley, Lisa; Tarasov, Alexey; Taylor, Martin; Theil, Florian: Packing twelve spherical caps to maximize tangencies (2013)
  20. Bourjaily, J.L.; Dire, A.; Shaikh, A.; Spradlin, M.; Volovich, A.: The soft-collinear bootstrap: $\mathcalN = 4$ Yang-Mills amplitudes at six- and seven-loops (2012)

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