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Small sets supporting fary embeddings of planar graphs

Authors:

Hubert de Fraysseix,

Richard PollackAuthors Info & Claims

STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing

Pages 426 - 433

https://doi.org/10.1145/62212.62254

Published: 01 January 1988 Publication History

Abstract

Answering a question of Rosenstiehl and Tarjan, we show that every plane graph with n vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n - 4 by n - 2 grid and provide an Ο(n) space, Ο(n log n) time algorithm to effect this embedding. The grid size is asymptotically optimal and it had been previously unknown whether one can always find a polynomial sized grid to support such an embedding. On the other hand we show that any set F, which can support a Fáry embedding of every planar graph of size n, has cardinality at least n + (1 - ο(1)) √n which settles a problem of Mohar.

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Cited By

Bekos MGronemann MMontecchiani FSymvonis A(2024)Convex grid drawings of planar graphs with constant edge-vertex resolutionTheoretical Computer Science10.1016/j.tcs.2023.114290982:COnline publication date: 8-Jan-2024
https://dl.acm.org/doi/10.1016/j.tcs.2023.114290
Da Lozzo GDi Battista GFrati FGrosso FPatrignani M(2024)Efficient Enumeration of Drawings and Combinatorial Structures for Maximal Planar GraphsWALCOM: Algorithms and Computation10.1007/978-981-97-0566-5_25(350-364)Online publication date: 29-Feb-2024
https://doi.org/10.1007/978-981-97-0566-5_25
Bernardi OFusy ÉLiang S(2024)A Schnyder-Type Drawing Algorithm for 5-Connected TriangulationsGraph Drawing and Network Visualization10.1007/978-3-031-49275-4_8(117-132)Online publication date: 6-Jan-2024
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Index Terms

Small sets supporting fary embeddings of planar graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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cover image ACM Conferences

STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing

January 1988

553 pages

ISBN:0897912640

DOI:10.1145/62212

Chairman:
J'anos Simon
Univ. of Chicago, Illinois

Copyright © 1988 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

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Published: 01 January 1988

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STOC88: 1988 Symposium on the Theory of Computing

May 2 - 4, 1988

Illinois, Chicago, USA

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STOC '88 Paper Acceptance Rate 53 of 192 submissions, 28%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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https://dl.acm.org/doi/10.1016/j.tcs.2023.114290
Da Lozzo GDi Battista GFrati FGrosso FPatrignani M(2024)Efficient Enumeration of Drawings and Combinatorial Structures for Maximal Planar GraphsWALCOM: Algorithms and Computation10.1007/978-981-97-0566-5_25(350-364)Online publication date: 29-Feb-2024
https://doi.org/10.1007/978-981-97-0566-5_25
Bernardi OFusy ÉLiang S(2024)A Schnyder-Type Drawing Algorithm for 5-Connected TriangulationsGraph Drawing and Network Visualization10.1007/978-3-031-49275-4_8(117-132)Online publication date: 6-Jan-2024
https://doi.org/10.1007/978-3-031-49275-4_8
Seemann CMoulton VStadler PHellmuth M(2023)Planar median graphs and cubesquare-graphsDiscrete Applied Mathematics10.1016/j.dam.2023.01.022331:C(38-58)Online publication date: 31-May-2023
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Brand CGanian RRöder SSchager F(2023)Fixed-Parameter Algorithms for Computing RAC Drawings of GraphsGraph Drawing and Network Visualization10.1007/978-3-031-49275-4_5(66-81)Online publication date: 20-Sep-2023
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Bekos MGronemann MMontecchiani FSymvonis A(2022)Convex Grid Drawings of Planar Graphs with Constant Edge-Vertex ResolutionCombinatorial Algorithms10.1007/978-3-031-06678-8_12(157-171)Online publication date: 29-May-2022
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Bekos MGronemann MMontecchiani FPálvölgyi DSymvonis ATheocharous L(2021)Grid drawings of graphs with constant edge-vertex resolutionComputational Geometry: Theory and Applications10.1016/j.comgeo.2021.10178998:COnline publication date: 1-Oct-2021
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Dieng YGavoille C(2020)On the Treewidth of Planar Minor Free GraphsInnovations and Interdisciplinary Solutions for Underserved Areas10.1007/978-3-030-51051-0_17(238-250)Online publication date: 6-Aug-2020
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Schlipf LSchmidt J(2019)Edge-OrdersAlgorithmica10.1007/s00453-018-0516-481:5(1881-1900)Online publication date: 1-May-2019
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