1-planar graph (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "1-planar graph" in English language version.

refsWebsite

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21doi.org

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15ams.org

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8semanticscholar.org

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5arxiv.org

69^th place

59^th place

3harvard.edu

18^th place

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1uni-lj.si

8,599^th place

8,200^th place

1combinatorics.org

low place

1maastrichtuniversity.nl

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1handle.net

102^nd place

76^th place

1arizona.edu

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ams.org

mathscinet.ams.org

Ringel, Gerhard (1965), "Ein Sechsfarbenproblem auf der Kugel", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German), 29 (1–2): 107–117, doi:10.1007/BF02996313, MR 0187232, S2CID 123286264.
Borodin, O. V. (1984), "Solution of the Ringel problem on vertex-face coloring of planar graphs and coloring of 1-planar graphs", Metody Diskretnogo Analiza (41): 12–26, 108, MR 0832128.
Albertson, Michael O.; Mohar, Bojan (2006), "Coloring vertices and faces of locally planar graphs" (PDF), Graphs and Combinatorics, 22 (3): 289–295, doi:10.1007/s00373-006-0653-4, MR 2264852, S2CID 1028234.
Schumacher, H. (1986), "Zur Struktur 1-planarer Graphen", Mathematische Nachrichten (in German), 125: 291–300, doi:10.1002/mana.19861250122, MR 0847368.
Czap, Július; Hudák, Dávid (2012), "1-planarity of complete multipartite graphs", Discrete Applied Mathematics, 160 (4–5): 505–512, doi:10.1016/j.dam.2011.11.014, MR 2876333.
Suzuki, Yusuke (2010), "Re-embeddings of maximum 1-planar graphs", SIAM Journal on Discrete Mathematics, 24 (4): 1527–1540, doi:10.1137/090746835, MR 2746706.
Didimo, Walter (2013), "Density of straight-line 1-planar graph drawings", Information Processing Letters, 113 (7): 236–240, doi:10.1016/j.ipl.2013.01.013, MR 3017985.
Grigoriev, Alexander; Bodlaender, Hans L. (2007), "Algorithms for graphs embeddable with few crossings per edge", Algorithmica, 49 (1): 1–11, doi:10.1007/s00453-007-0010-x, hdl:1874/17980, MR 2344391, S2CID 8174422.
Eggleton, Roger B. (1986), "Rectilinear drawings of graphs", Utilitas Mathematica, 29: 149–172, MR 0846198.
Thomassen, Carsten (1988), "Rectilinear drawings of graphs", Journal of Graph Theory, 12 (3): 335–341, doi:10.1002/jgt.3190120306, MR 0956195.
Dehkordi, Hooman Reisi; Eades, Peter (2012), "Every outer-1-plane graph has a right angle crossing drawing", International Journal of Computational Geometry & Applications, 22 (6): 543–557, doi:10.1142/S021819591250015X, MR 3042921.
Chen, Zhi-Zhong; Grigni, Michelangelo; Papadimitriou, Christos H. (2002), "Map graphs", Journal of the ACM, 49 (2): 127–138, arXiv:cs/9910013, doi:10.1145/506147.506148, MR 2147819, S2CID 2657838.
Kainen, Paul (1973), "Thickness and coarseness of graphs", Abh. Math. Sem. Univ. Hamburg, 39: 88–95, doi:10.1007/BF02992822, MR 0335322, S2CID 121667358.
Pach, János; Tóth, Géza (1997), "Graphs drawn with few crossings per edge", Combinatorica, 17 (3): 427–439, doi:10.1007/BF01215922, MR 1606052, S2CID 20480170.
Nešetřil, Jaroslav; Ossona de Mendez, Patrice (2012), Sparsity: Graphs, Structures, and Algorithms, Algorithms and Combinatorics, vol. 28, Springer, Theorem 14.4, p. 321, doi:10.1007/978-3-642-27875-4, ISBN 978-3-642-27874-7, MR 2920058.

arizona.edu

cs.arizona.edu

Alam, Md. Jawaherul; Brandenburg, Franz J.; Kobourov, Stephen G. (2013), "Straight-line grid drawings of 3-connected 1-planar graphs", Graph Drawing: 21st International Symposium, GD 2013, Bordeaux, France, September 23-25, 2013, Revised Selected Papers (PDF), Lecture Notes in Computer Science, vol. 8242, pp. 83–94, doi:10.1007/978-3-319-03841-4_8, ISBN 978-3-319-03840-7.

arxiv.org

Korzhik, Vladimir P.; Mohar, Bojan (2009), "Minimal obstructions for 1-immersions and hardness of 1-planarity testing", in Tollis, Ioannis G.; Patrignani, Maurizio (eds.), Graph Drawing: 16th International Symposium, GD 2008, Heraklion, Crete, Greece, September 21-24, 2008, Revised Papers, Lecture Notes in Computer Science, vol. 5417, Springer, pp. 302–312, arXiv:1110.4881, doi:10.1007/978-3-642-00219-9_29, ISBN 978-3-642-00218-2, S2CID 13436158.
Cabello, Sergio; Mohar, Bojan (2012), Adding one edge to planar graphs makes crossing number and 1-planarity hard, arXiv:1203.5944, Bibcode:2012arXiv1203.5944C. Expanded version of a paper from the 17th ACM Symposium on Computational Geometry, 2010.
Bannister, Michael J.; Cabello, Sergio; Eppstein, David (2013), "Parameterized complexity of 1-planarity", Algorithms and Data Structures Symposium (WADS 2013), vol. 22, pp. 23–49, arXiv:1304.5591, Bibcode:2013arXiv1304.5591B, doi:10.7155/jgaa.00457, S2CID 4417962.
Chen, Zhi-Zhong; Grigni, Michelangelo; Papadimitriou, Christos H. (2002), "Map graphs", Journal of the ACM, 49 (2): 127–138, arXiv:cs/9910013, doi:10.1145/506147.506148, MR 2147819, S2CID 2657838.
Dujmović, Vida; Eppstein, David; Wood, David R. (2015), "Genus, treewidth, and local crossing number", Proc. 23rd International Symposium on Graph Drawing and Network Visualization (GD 2015), pp. 77–88, arXiv:1506.04380, Bibcode:2015arXiv150604380D.

combinatorics.org

Czap, Július; Hudák, Dávid (2013), "On drawings and decompositions of 1-planar graphs", Electronic Journal of Combinatorics, 20 (2), P54, doi:10.37236/2392.

doi.org

Ringel, Gerhard (1965), "Ein Sechsfarbenproblem auf der Kugel", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German), 29 (1–2): 107–117, doi:10.1007/BF02996313, MR 0187232, S2CID 123286264.
Albertson, Michael O.; Mohar, Bojan (2006), "Coloring vertices and faces of locally planar graphs" (PDF), Graphs and Combinatorics, 22 (3): 289–295, doi:10.1007/s00373-006-0653-4, MR 2264852, S2CID 1028234.
Schumacher, H. (1986), "Zur Struktur 1-planarer Graphen", Mathematische Nachrichten (in German), 125: 291–300, doi:10.1002/mana.19861250122, MR 0847368.
Czap, Július; Hudák, Dávid (2013), "On drawings and decompositions of 1-planar graphs", Electronic Journal of Combinatorics, 20 (2), P54, doi:10.37236/2392.
Czap, Július; Hudák, Dávid (2012), "1-planarity of complete multipartite graphs", Discrete Applied Mathematics, 160 (4–5): 505–512, doi:10.1016/j.dam.2011.11.014, MR 2876333.
Suzuki, Yusuke (2010), "Re-embeddings of maximum 1-planar graphs", SIAM Journal on Discrete Mathematics, 24 (4): 1527–1540, doi:10.1137/090746835, MR 2746706.
Didimo, Walter (2013), "Density of straight-line 1-planar graph drawings", Information Processing Letters, 113 (7): 236–240, doi:10.1016/j.ipl.2013.01.013, MR 3017985.
Grigoriev, Alexander; Bodlaender, Hans L. (2007), "Algorithms for graphs embeddable with few crossings per edge", Algorithmica, 49 (1): 1–11, doi:10.1007/s00453-007-0010-x, hdl:1874/17980, MR 2344391, S2CID 8174422.
Korzhik, Vladimir P.; Mohar, Bojan (2009), "Minimal obstructions for 1-immersions and hardness of 1-planarity testing", in Tollis, Ioannis G.; Patrignani, Maurizio (eds.), Graph Drawing: 16th International Symposium, GD 2008, Heraklion, Crete, Greece, September 21-24, 2008, Revised Papers, Lecture Notes in Computer Science, vol. 5417, Springer, pp. 302–312, arXiv:1110.4881, doi:10.1007/978-3-642-00219-9_29, ISBN 978-3-642-00218-2, S2CID 13436158.
Bannister, Michael J.; Cabello, Sergio; Eppstein, David (2013), "Parameterized complexity of 1-planarity", Algorithms and Data Structures Symposium (WADS 2013), vol. 22, pp. 23–49, arXiv:1304.5591, Bibcode:2013arXiv1304.5591B, doi:10.7155/jgaa.00457, S2CID 4417962.
Thomassen, Carsten (1988), "Rectilinear drawings of graphs", Journal of Graph Theory, 12 (3): 335–341, doi:10.1002/jgt.3190120306, MR 0956195.
Hong, Seok-Hee; Eades, Peter; Liotta, Giuseppe; Poon, Sheung-Hung (2012), "Fáry's theorem for 1-planar graphs", in Gudmundsson, Joachim; Mestre, Julián; Viglas, Taso (eds.), Computing and Combinatorics: 18th Annual International Conference, COCOON 2012, Sydney, Australia, August 20-22, 2012, Proceedings, Lecture Notes in Computer Science, vol. 7434, Springer, pp. 335–346, doi:10.1007/978-3-642-32241-9_29, ISBN 978-3-642-32240-2.
Alam, Md. Jawaherul; Brandenburg, Franz J.; Kobourov, Stephen G. (2013), "Straight-line grid drawings of 3-connected 1-planar graphs", Graph Drawing: 21st International Symposium, GD 2013, Bordeaux, France, September 23-25, 2013, Revised Selected Papers (PDF), Lecture Notes in Computer Science, vol. 8242, pp. 83–94, doi:10.1007/978-3-319-03841-4_8, ISBN 978-3-319-03840-7.
Bekos, Michael A.; Bruckdorfer, Till; Kaufmann, Michael; Raftopoulou, Chrysanthi (2015), "1-Planar graphs have constant book thickness", Algorithms – ESA 2015, Lecture Notes in Computer Science, vol. 9294, Springer, pp. 130–141, doi:10.1007/978-3-662-48350-3_12, ISBN 978-3-662-48349-7.
Dehkordi, Hooman Reisi; Eades, Peter (2012), "Every outer-1-plane graph has a right angle crossing drawing", International Journal of Computational Geometry & Applications, 22 (6): 543–557, doi:10.1142/S021819591250015X, MR 3042921.
Hong, Seok-Hee; Eades, Peter; Katoh, Naoki; Liotta, Giuseppe; Schweitzer, Pascal; Suzuki, Yusuke (2013), "A linear-time algorithm for testing outer-1-planarity", in Wismath, Stephen; Wolff, Alexander (eds.), 21st International Symposium, GD 2013, Bordeaux, France, September 23-25, 2013, Revised Selected Papers, Lecture Notes in Computer Science, vol. 8242, pp. 71–82, doi:10.1007/978-3-319-03841-4_7, ISBN 978-3-319-03840-7.
Auer, Christopher; Bachmaier, Christian; Brandenburg, Franz J.; Gleißner, Andreas; Hanauer, Kathrin; Neuwirth, Daniel; Reislhuber, Josef (2013), "Recognizing outer 1-planar graphs in linear time", in Wismath, Stephen; Wolff, Alexander (eds.), 21st International Symposium, GD 2013, Bordeaux, France, September 23-25, 2013, Revised Selected Papers, Lecture Notes in Computer Science, vol. 8242, pp. 107–118, doi:10.1007/978-3-319-03841-4_10, ISBN 978-3-319-03840-7.
Chen, Zhi-Zhong; Grigni, Michelangelo; Papadimitriou, Christos H. (2002), "Map graphs", Journal of the ACM, 49 (2): 127–138, arXiv:cs/9910013, doi:10.1145/506147.506148, MR 2147819, S2CID 2657838.
Kainen, Paul (1973), "Thickness and coarseness of graphs", Abh. Math. Sem. Univ. Hamburg, 39: 88–95, doi:10.1007/BF02992822, MR 0335322, S2CID 121667358.
Pach, János; Tóth, Géza (1997), "Graphs drawn with few crossings per edge", Combinatorica, 17 (3): 427–439, doi:10.1007/BF01215922, MR 1606052, S2CID 20480170.
Nešetřil, Jaroslav; Ossona de Mendez, Patrice (2012), Sparsity: Graphs, Structures, and Algorithms, Algorithms and Combinatorics, vol. 28, Springer, Theorem 14.4, p. 321, doi:10.1007/978-3-642-27875-4, ISBN 978-3-642-27874-7, MR 2920058.

handle.net

hdl.handle.net

Grigoriev, Alexander; Bodlaender, Hans L. (2007), "Algorithms for graphs embeddable with few crossings per edge", Algorithmica, 49 (1): 1–11, doi:10.1007/s00453-007-0010-x, hdl:1874/17980, MR 2344391, S2CID 8174422.

harvard.edu

ui.adsabs.harvard.edu

Cabello, Sergio; Mohar, Bojan (2012), Adding one edge to planar graphs makes crossing number and 1-planarity hard, arXiv:1203.5944, Bibcode:2012arXiv1203.5944C. Expanded version of a paper from the 17th ACM Symposium on Computational Geometry, 2010.
Bannister, Michael J.; Cabello, Sergio; Eppstein, David (2013), "Parameterized complexity of 1-planarity", Algorithms and Data Structures Symposium (WADS 2013), vol. 22, pp. 23–49, arXiv:1304.5591, Bibcode:2013arXiv1304.5591B, doi:10.7155/jgaa.00457, S2CID 4417962.
Dujmović, Vida; Eppstein, David; Wood, David R. (2015), "Genus, treewidth, and local crossing number", Proc. 23rd International Symposium on Graph Drawing and Network Visualization (GD 2015), pp. 77–88, arXiv:1506.04380, Bibcode:2015arXiv150604380D.

maastrichtuniversity.nl

cris.maastrichtuniversity.nl

Grigoriev, Alexander; Bodlaender, Hans L. (2007), "Algorithms for graphs embeddable with few crossings per edge", Algorithmica, 49 (1): 1–11, doi:10.1007/s00453-007-0010-x, hdl:1874/17980, MR 2344391, S2CID 8174422.

semanticscholar.org

api.semanticscholar.org

Ringel, Gerhard (1965), "Ein Sechsfarbenproblem auf der Kugel", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German), 29 (1–2): 107–117, doi:10.1007/BF02996313, MR 0187232, S2CID 123286264.
Albertson, Michael O.; Mohar, Bojan (2006), "Coloring vertices and faces of locally planar graphs" (PDF), Graphs and Combinatorics, 22 (3): 289–295, doi:10.1007/s00373-006-0653-4, MR 2264852, S2CID 1028234.
Grigoriev, Alexander; Bodlaender, Hans L. (2007), "Algorithms for graphs embeddable with few crossings per edge", Algorithmica, 49 (1): 1–11, doi:10.1007/s00453-007-0010-x, hdl:1874/17980, MR 2344391, S2CID 8174422.
Korzhik, Vladimir P.; Mohar, Bojan (2009), "Minimal obstructions for 1-immersions and hardness of 1-planarity testing", in Tollis, Ioannis G.; Patrignani, Maurizio (eds.), Graph Drawing: 16th International Symposium, GD 2008, Heraklion, Crete, Greece, September 21-24, 2008, Revised Papers, Lecture Notes in Computer Science, vol. 5417, Springer, pp. 302–312, arXiv:1110.4881, doi:10.1007/978-3-642-00219-9_29, ISBN 978-3-642-00218-2, S2CID 13436158.
Bannister, Michael J.; Cabello, Sergio; Eppstein, David (2013), "Parameterized complexity of 1-planarity", Algorithms and Data Structures Symposium (WADS 2013), vol. 22, pp. 23–49, arXiv:1304.5591, Bibcode:2013arXiv1304.5591B, doi:10.7155/jgaa.00457, S2CID 4417962.
Chen, Zhi-Zhong; Grigni, Michelangelo; Papadimitriou, Christos H. (2002), "Map graphs", Journal of the ACM, 49 (2): 127–138, arXiv:cs/9910013, doi:10.1145/506147.506148, MR 2147819, S2CID 2657838.
Kainen, Paul (1973), "Thickness and coarseness of graphs", Abh. Math. Sem. Univ. Hamburg, 39: 88–95, doi:10.1007/BF02992822, MR 0335322, S2CID 121667358.
Pach, János; Tóth, Géza (1997), "Graphs drawn with few crossings per edge", Combinatorica, 17 (3): 427–439, doi:10.1007/BF01215922, MR 1606052, S2CID 20480170.

uni-lj.si

fmf.uni-lj.si

Albertson, Michael O.; Mohar, Bojan (2006), "Coloring vertices and faces of locally planar graphs" (PDF), Graphs and Combinatorics, 22 (3): 289–295, doi:10.1007/s00373-006-0653-4, MR 2264852, S2CID 1028234.