References
- B.M. Ábrego, R. Fabila-Monroy, S. Fernández-Merchant, D. Flores-Peñaloza, F. Hurtado, V. Sacristán, and M. Saumell, On crossing numbers of geometric proximity graphs, Comput. Geom. 44 (2011), pp. 216–233. https://doi.org/10.1016/j.comgeo.2010.11.003
- S. Bereg, S. -H. Hong, N. Katoh, S. -H. Poon, and S. Tanigawa, On the edge crossing properties of Euclidean minimum weight Laman graphs, Comput. Geom. Theory Appl. 51 (2016), pp. 15–24. https://doi.org/10.1016/j.comgeo.2015.10.002
- P. Bose, S. Collette, F. Hurtado, M. Korman, S. Langerman, V. Sacristán, and M. Saumell, Some properties of k-Delaunay and k-Gabriel graphs, Comput. Geom. 46 (2013), pp. 131–139. https://doi.org/10.1016/j.comgeo.2012.04.006
- J. Graver, B. Servatius, and H. Servatius, Combinatorial Rigidity, Graduate Studies in Mathematics, vol. 2, American Mathematical Society, 1993.
- H. Grötzsch, Zur theorie der diskreten gebilde. VII. Ein dreifarbensatz für dreikreisfreie netze auf der kugel, Wiss. Z. Martin-Luther-U., Halle-Wittenberg, Math.-Nat. Reihe 8 (1959), pp. 109–120.
- J. Kleinberg and É. Tardos, Algorithm Design, Pearson Education India, 2006.
- Y. Koabayashi, Y. Higashikawa, and N. Katoh, Improving upper and lower bounds for the total number of edge crossings of euclidean minimum weight Laman graphs, in International Computing and Combinatorics Conference, 2021, pp. 244–256. https://doi.org/10.1007/978-3-030-89543-3_21
- A. Lee and I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (2008), pp. 1425–1437. https://doi.org/10.1016/j.disc.2007.07.104
- J.G. Oxley, Matroid Theory, Oxford University Press, USA, 2006.
- G. Laman, On graphs and rigidity of plane skeletal structures, J. Eng. Math. 4 (1970), pp. 331–340. https://doi.org/10.1007/BF01534980
- B. Servatius, The geometry of frameworks: Rigidity, mechanisms and cad, in Geometry at Work: A Collection of Papers Showing Applications of Geometry, C.A. Gorini, Ed., Cambridge University Press, 2000.
- T.H. Su and R.C. Chang, The k-Gabriel graphs and their applications. in International Symposium on Algorithms, 1990, pp. 66–75.https://doi.org/10.1007/3-540-52921-7_56
- M.F. Thorpe and P.M. Duxbury, (eds.), Rigidity Theory and Applications, Kluwer Academic/Plenum Publishers, New York, 1999. https://doi.org/10.1007/b115749
- A.C. Yao, On constructing minimum spanning trees in k-dimensional space and related problems, SIAM J. Comput. 11 (1982), pp. 721–736. https://doi.org/10.1137/0211059