Slope number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Slope number" in English language version.

refsWebsite

Global rank English rank

6doi.org

2^nd place

5ams.org

451^st place

277^th place

2arxiv.org

69^th place

59^th place

1combinatorics.org

low place

1handle.net

102^nd place

76^th place

ams.org

mathscinet.ams.org

Proved independently by Barát, Matoušek & Wood (2006) and Pach & Pálvölgyi (2006), solving a problem posed by Dujmović, Suderman & Wood (2005). See theorems 5.1 and 5.2 of Pach & Sharir (2009). Pach, János; Pálvölgyi, Dömötör (2006), "Bounded-degree graphs can have arbitrarily large slope numbers", Electronic Journal of Combinatorics, 13 (1): N1, MR 2200545. Dujmović, Vida; Suderman, Matthew; Wood, David R. (2005), "Really straight graph drawings", in Pach, János (ed.), Graph Drawing: 12th International Symposium, GD 2004, New York, NY, USA, September 29-October 2, 2004, Revised Selected Papers, Lecture Notes in Computer Science, vol. 3383, Berlin: Springer-Verlag, pp. 122–132, arXiv:cs/0405112, doi:10.1007/978-3-540-31843-9_14. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.
Mukkamala & Szegedy (2009), improving an earlier result of Keszegh et al. (2008); theorem 5.3 of Pach & Sharir (2009). Mukkamala, Padmini; Szegedy, Mario (2009), "Geometric representation of cubic graphs with four directions", Computational Geometry: Theory and Applications, 42 (9): 842–851, doi:10.1016/j.comgeo.2009.01.005, MR 2543806. Keszegh, Balázs; Pach, János; Pálvölgyi, Dömötör; Tóth, Géza (2008), "Drawing cubic graphs with at most five slopes", Computational Geometry: Theory and Applications, 40 (2): 138–147, doi:10.1016/j.comgeo.2007.05.003, MR 2400539. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.
Hansen (1988). Hansen, Lowell J. (1988), "On the Rodin and Sullivan ring lemma", Complex Variables, Theory and Application, 10 (1): 23–30, doi:10.1080/17476938808814284, MR 0946096.
Formann et al. (1993); Eades, Hong & Poon (2010); Maňuch et al. (2011). Formann, M.; Hagerup, T.; Haralambides, J.; Kaufmann, M.; Leighton, F. T.; Symvonis, A.; Welzl, E.; Woeginger, G. (1993), "Drawing graphs in the plane with high resolution", SIAM Journal on Computing, 22 (5): 1035–1052, doi:10.1137/0222063, MR 1237161. Eades, Peter; Hong, Seok-Hee; Poon, Sheung-Hung (2010), "On rectilinear drawing of graphs", in Eppstein, David; Gansner, Emden R. (eds.), Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009, Revised Papers, Lecture Notes in Computer Science, vol. 5849, Berlin: Springer, pp. 232–243, doi:10.1007/978-3-642-11805-0_23, MR 2680455. Maňuch, Ján; Patterson, Murray; Poon, Sheung-Hung; Thachuk, Chris (2011), "Complexity of finding non-planar rectilinear drawings of graphs", in Brandes, Ulrik; Cornelsen, Sabine (eds.), Graph Drawing: 18th International Symposium, GD 2010, Konstanz, Germany, September 21-24, 2010, Revised Selected Papers, Lecture Notes in Computer Science, vol. 6502, Heidelberg: Springer, pp. 305–316, doi:10.1007/978-3-642-18469-7_28, hdl:10281/217381, MR 2781275.
Garg & Tamassia (2001). Garg, Ashim; Tamassia, Roberto (2001), "On the computational complexity of upward and rectilinear planarity testing", SIAM Journal on Computing, 31 (2): 601–625, doi:10.1137/S0097539794277123, MR 1861292.

arxiv.org

Proved independently by Barát, Matoušek & Wood (2006) and Pach & Pálvölgyi (2006), solving a problem posed by Dujmović, Suderman & Wood (2005). See theorems 5.1 and 5.2 of Pach & Sharir (2009). Pach, János; Pálvölgyi, Dömötör (2006), "Bounded-degree graphs can have arbitrarily large slope numbers", Electronic Journal of Combinatorics, 13 (1): N1, MR 2200545. Dujmović, Vida; Suderman, Matthew; Wood, David R. (2005), "Really straight graph drawings", in Pach, János (ed.), Graph Drawing: 12th International Symposium, GD 2004, New York, NY, USA, September 29-October 2, 2004, Revised Selected Papers, Lecture Notes in Computer Science, vol. 3383, Berlin: Springer-Verlag, pp. 122–132, arXiv:cs/0405112, doi:10.1007/978-3-540-31843-9_14. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.
Mukkamala & Pálvölgyi (2012). Mukkamala, Padmini; Pálvölgyi, Dömötör (2012), "Drawing cubic graphs with the four basic slopes", in van Kreveld, Marc; Speckmann, Bettina (eds.), Graph Drawing: 19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 21-23, 2011, Revised Selected Papers, Lecture Notes in Computer Science, vol. 7034, Springer, pp. 254–265, arXiv:1106.1973, doi:10.1007/978-3-642-25878-7_25.

combinatorics.org

Proved independently by Barát, Matoušek & Wood (2006) and Pach & Pálvölgyi (2006), solving a problem posed by Dujmović, Suderman & Wood (2005). See theorems 5.1 and 5.2 of Pach & Sharir (2009). Pach, János; Pálvölgyi, Dömötör (2006), "Bounded-degree graphs can have arbitrarily large slope numbers", Electronic Journal of Combinatorics, 13 (1): N1, MR 2200545. Dujmović, Vida; Suderman, Matthew; Wood, David R. (2005), "Really straight graph drawings", in Pach, János (ed.), Graph Drawing: 12th International Symposium, GD 2004, New York, NY, USA, September 29-October 2, 2004, Revised Selected Papers, Lecture Notes in Computer Science, vol. 3383, Berlin: Springer-Verlag, pp. 122–132, arXiv:cs/0405112, doi:10.1007/978-3-540-31843-9_14. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.

doi.org

Proved independently by Barát, Matoušek & Wood (2006) and Pach & Pálvölgyi (2006), solving a problem posed by Dujmović, Suderman & Wood (2005). See theorems 5.1 and 5.2 of Pach & Sharir (2009). Pach, János; Pálvölgyi, Dömötör (2006), "Bounded-degree graphs can have arbitrarily large slope numbers", Electronic Journal of Combinatorics, 13 (1): N1, MR 2200545. Dujmović, Vida; Suderman, Matthew; Wood, David R. (2005), "Really straight graph drawings", in Pach, János (ed.), Graph Drawing: 12th International Symposium, GD 2004, New York, NY, USA, September 29-October 2, 2004, Revised Selected Papers, Lecture Notes in Computer Science, vol. 3383, Berlin: Springer-Verlag, pp. 122–132, arXiv:cs/0405112, doi:10.1007/978-3-540-31843-9_14. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.
Mukkamala & Szegedy (2009), improving an earlier result of Keszegh et al. (2008); theorem 5.3 of Pach & Sharir (2009). Mukkamala, Padmini; Szegedy, Mario (2009), "Geometric representation of cubic graphs with four directions", Computational Geometry: Theory and Applications, 42 (9): 842–851, doi:10.1016/j.comgeo.2009.01.005, MR 2543806. Keszegh, Balázs; Pach, János; Pálvölgyi, Dömötör; Tóth, Géza (2008), "Drawing cubic graphs with at most five slopes", Computational Geometry: Theory and Applications, 40 (2): 138–147, doi:10.1016/j.comgeo.2007.05.003, MR 2400539. Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol. 152, American Mathematical Society, pp. 126–127.
Mukkamala & Pálvölgyi (2012). Mukkamala, Padmini; Pálvölgyi, Dömötör (2012), "Drawing cubic graphs with the four basic slopes", in van Kreveld, Marc; Speckmann, Bettina (eds.), Graph Drawing: 19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 21-23, 2011, Revised Selected Papers, Lecture Notes in Computer Science, vol. 7034, Springer, pp. 254–265, arXiv:1106.1973, doi:10.1007/978-3-642-25878-7_25.
Hansen (1988). Hansen, Lowell J. (1988), "On the Rodin and Sullivan ring lemma", Complex Variables, Theory and Application, 10 (1): 23–30, doi:10.1080/17476938808814284, MR 0946096.
Formann et al. (1993); Eades, Hong & Poon (2010); Maňuch et al. (2011). Formann, M.; Hagerup, T.; Haralambides, J.; Kaufmann, M.; Leighton, F. T.; Symvonis, A.; Welzl, E.; Woeginger, G. (1993), "Drawing graphs in the plane with high resolution", SIAM Journal on Computing, 22 (5): 1035–1052, doi:10.1137/0222063, MR 1237161. Eades, Peter; Hong, Seok-Hee; Poon, Sheung-Hung (2010), "On rectilinear drawing of graphs", in Eppstein, David; Gansner, Emden R. (eds.), Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009, Revised Papers, Lecture Notes in Computer Science, vol. 5849, Berlin: Springer, pp. 232–243, doi:10.1007/978-3-642-11805-0_23, MR 2680455. Maňuch, Ján; Patterson, Murray; Poon, Sheung-Hung; Thachuk, Chris (2011), "Complexity of finding non-planar rectilinear drawings of graphs", in Brandes, Ulrik; Cornelsen, Sabine (eds.), Graph Drawing: 18th International Symposium, GD 2010, Konstanz, Germany, September 21-24, 2010, Revised Selected Papers, Lecture Notes in Computer Science, vol. 6502, Heidelberg: Springer, pp. 305–316, doi:10.1007/978-3-642-18469-7_28, hdl:10281/217381, MR 2781275.
Garg & Tamassia (2001). Garg, Ashim; Tamassia, Roberto (2001), "On the computational complexity of upward and rectilinear planarity testing", SIAM Journal on Computing, 31 (2): 601–625, doi:10.1137/S0097539794277123, MR 1861292.

handle.net

hdl.handle.net

Formann et al. (1993); Eades, Hong & Poon (2010); Maňuch et al. (2011). Formann, M.; Hagerup, T.; Haralambides, J.; Kaufmann, M.; Leighton, F. T.; Symvonis, A.; Welzl, E.; Woeginger, G. (1993), "Drawing graphs in the plane with high resolution", SIAM Journal on Computing, 22 (5): 1035–1052, doi:10.1137/0222063, MR 1237161. Eades, Peter; Hong, Seok-Hee; Poon, Sheung-Hung (2010), "On rectilinear drawing of graphs", in Eppstein, David; Gansner, Emden R. (eds.), Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009, Revised Papers, Lecture Notes in Computer Science, vol. 5849, Berlin: Springer, pp. 232–243, doi:10.1007/978-3-642-11805-0_23, MR 2680455. Maňuch, Ján; Patterson, Murray; Poon, Sheung-Hung; Thachuk, Chris (2011), "Complexity of finding non-planar rectilinear drawings of graphs", in Brandes, Ulrik; Cornelsen, Sabine (eds.), Graph Drawing: 18th International Symposium, GD 2010, Konstanz, Germany, September 21-24, 2010, Revised Selected Papers, Lecture Notes in Computer Science, vol. 6502, Heidelberg: Springer, pp. 305–316, doi:10.1007/978-3-642-18469-7_28, hdl:10281/217381, MR 2781275.