Reprint of: Upward planar embedding of an n-vertex oriented path on O(n2) points
We prove that every n-vertex oriented path admits an upward planar embedding on every general set of (n−1)2+1 points on the plane. This result improves the previously known upper bound which is exponential in the number of switches of the given oriented path (Angelini et al. 2010) [1].
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Published in | Computational geometry : theory and applications Vol. 47; no. 3; pp. 493 - 498 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.04.2014
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Subjects | |
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Abstract | We prove that every n-vertex oriented path admits an upward planar embedding on every general set of (n−1)2+1 points on the plane. This result improves the previously known upper bound which is exponential in the number of switches of the given oriented path (Angelini et al. 2010) [1]. |
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AbstractList | We prove that every n-vertex oriented path admits an upward planar embedding on every general set of (n−1)2+1 points on the plane. This result improves the previously known upper bound which is exponential in the number of switches of the given oriented path (Angelini et al. 2010) [1]. |
Author | Mchedlidze, Tamara |
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Cites_doi | 10.1006/jctb.1999.1945 10.1016/j.comgeo.2009.07.002 10.1090/S0002-9947-1986-0837805-6 10.1016/0095-8956(72)90035-4 10.2307/2323956 10.1007/BF02187887 |
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References | Jørgen Bang-Jensen, Gregory Gutin, Paths, trees and cycles in tournaments, Technical report. Rosenfeld (br0090) 1972; 12 Kaufmann, Mchedlidze, Symvonis (br0080) 2011 Thomason (br0100) 1986; 296 Binucci, Di Giacomo, Didimo, Estrella-Balderrama, Frati, Kobourov, Liotta (br0030) 2010; 43 Geyer, Kaufmann, Mchedlidze, Symvonis (br0040) 2011 Gritzmann, Mohar, Pach, Pollack (br0050) 1991; 98 Angelini, Frati, Geyer, Kaufmann, Mchedlidze, Symvonis (br0010) 2010 Hayward (br0070) 1987; 2 Havet, Thomasse (br0060) 2000; 78 Havet (10.1016/j.comgeo.2013.11.007_br0060) 2000; 78 Rosenfeld (10.1016/j.comgeo.2013.11.007_br0090) 1972; 12 Hayward (10.1016/j.comgeo.2013.11.007_br0070) 1987; 2 Gritzmann (10.1016/j.comgeo.2013.11.007_br0050) 1991; 98 Kaufmann (10.1016/j.comgeo.2013.11.007_br0080) 2011 Geyer (10.1016/j.comgeo.2013.11.007_br0040) 2011 Angelini (10.1016/j.comgeo.2013.11.007_br0010) 2010 10.1016/j.comgeo.2013.11.007_br0020 Binucci (10.1016/j.comgeo.2013.11.007_br0030) 2010; 43 Thomason (10.1016/j.comgeo.2013.11.007_br0100) 1986; 296 |
References_xml | – volume: 2 start-page: 327 year: 1987 end-page: 343 ident: br0070 article-title: A lower bound for the optimal crossing-free hamiltonian cycle problem publication-title: Discrete & Computational Geometry contributor: fullname: Hayward – volume: 78 start-page: 243 year: 2000 end-page: 273 ident: br0060 article-title: Oriented hamiltonian paths in tournaments: A proof of Rosenfeldʼs conjecture publication-title: Journal of Combinatorial Theory Series B contributor: fullname: Thomasse – start-page: 25 year: 2010 end-page: 37 ident: br0010 article-title: Upward geometric graph embeddings into point sets publication-title: 18th International Symposium on Graph Drawing (GDʼ10) contributor: fullname: Symvonis – start-page: 403 year: 2011 end-page: 414 ident: br0080 article-title: Upward point set embeddability for convex point sets is in P publication-title: 19th International Symposium on Graph Drawing (GD ʼ11) contributor: fullname: Symvonis – volume: 12 start-page: 93 year: 1972 end-page: 99 ident: br0090 article-title: Antidirected hamiltonian paths in tournaments publication-title: Journal of Combinatorial Theory Series B contributor: fullname: Rosenfeld – volume: 98 start-page: 165 year: 1991 end-page: 166 ident: br0050 article-title: Embedding a planar triangulation with vertices at specified points publication-title: The American Mathematical Monthly contributor: fullname: Pollack – start-page: 272 year: 2011 end-page: 283 ident: br0040 article-title: Upward point-set embeddability publication-title: 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEMʼ11) contributor: fullname: Symvonis – volume: 296 start-page: 167 year: 1986 end-page: 180 ident: br0100 article-title: Paths and cycles in tournaments publication-title: Transactions of the American Mathematical Society contributor: fullname: Thomason – volume: 43 start-page: 219 year: 2010 end-page: 232 ident: br0030 article-title: Upward straight-line embeddings of directed graphs into point sets publication-title: Computational Geometry contributor: fullname: Liotta – volume: 78 start-page: 243 issue: 2 year: 2000 ident: 10.1016/j.comgeo.2013.11.007_br0060 article-title: Oriented hamiltonian paths in tournaments: A proof of Rosenfeldʼs conjecture publication-title: Journal of Combinatorial Theory Series B doi: 10.1006/jctb.1999.1945 contributor: fullname: Havet – volume: 43 start-page: 219 year: 2010 ident: 10.1016/j.comgeo.2013.11.007_br0030 article-title: Upward straight-line embeddings of directed graphs into point sets publication-title: Computational Geometry doi: 10.1016/j.comgeo.2009.07.002 contributor: fullname: Binucci – volume: 296 start-page: 167 year: 1986 ident: 10.1016/j.comgeo.2013.11.007_br0100 article-title: Paths and cycles in tournaments publication-title: Transactions of the American Mathematical Society doi: 10.1090/S0002-9947-1986-0837805-6 contributor: fullname: Thomason – start-page: 25 year: 2010 ident: 10.1016/j.comgeo.2013.11.007_br0010 article-title: Upward geometric graph embeddings into point sets contributor: fullname: Angelini – ident: 10.1016/j.comgeo.2013.11.007_br0020 – start-page: 403 year: 2011 ident: 10.1016/j.comgeo.2013.11.007_br0080 article-title: Upward point set embeddability for convex point sets is in P contributor: fullname: Kaufmann – volume: 12 start-page: 93 year: 1972 ident: 10.1016/j.comgeo.2013.11.007_br0090 article-title: Antidirected hamiltonian paths in tournaments publication-title: Journal of Combinatorial Theory Series B doi: 10.1016/0095-8956(72)90035-4 contributor: fullname: Rosenfeld – start-page: 272 year: 2011 ident: 10.1016/j.comgeo.2013.11.007_br0040 article-title: Upward point-set embeddability contributor: fullname: Geyer – volume: 98 start-page: 165 year: 1991 ident: 10.1016/j.comgeo.2013.11.007_br0050 article-title: Embedding a planar triangulation with vertices at specified points publication-title: The American Mathematical Monthly doi: 10.2307/2323956 contributor: fullname: Gritzmann – volume: 2 start-page: 327 year: 1987 ident: 10.1016/j.comgeo.2013.11.007_br0070 article-title: A lower bound for the optimal crossing-free hamiltonian cycle problem publication-title: Discrete & Computational Geometry doi: 10.1007/BF02187887 contributor: fullname: Hayward |
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Snippet | We prove that every n-vertex oriented path admits an upward planar embedding on every general set of (n−1)2+1 points on the plane. This result improves the... |
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SubjectTerms | Oriented path Universal point set Upward point-set embedding |
Title | Reprint of: Upward planar embedding of an n-vertex oriented path on O(n2) points |
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