article

Map graphs

Authors:

Zhi-Zhong Chen,

Michelangelo Grigni,

Christos H. PapadimitriouAuthors Info & Claims

Journal of the ACM (JACM), Volume 49, Issue 2

Pages 127 - 138

https://doi.org/10.1145/506147.506148

Published: 01 March 2002 Publication History

Abstract

We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, derive some consequences regarding sparsity and coloring, and survey some algorithmic results.

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Index Terms

Map graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems
  2. Randomness, geometry and discrete structures

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 49, Issue 2

March 2002

162 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/506147

Issue’s Table of Contents

Copyright © 2002 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 2002

Published in JACM Volume 49, Issue 2

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Cited By

Bekos MDa Lozzo GGriesbach SGronemann MMontecchiani FRaftopoulou C(2024)Book embeddings of k-framed graphs and k-map graphsDiscrete Mathematics10.1016/j.disc.2023.113690347:1(113690)Online publication date: Jan-2024
https://doi.org/10.1016/j.disc.2023.113690
Wang PZecchin AMaier H(2023)Improved selection strategy for multi‐objective evolutionary algorithms with application to water distribution optimization problemsComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1296438:10(1290-1306)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1111/mice.12964
Song LWang CFan JLu H(2023)Elastic structural analysis based on graph neural network without labeled dataComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1294438:10(1307-1323)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1111/mice.12944
Dujmović VMorin PWood D(2023)Graph product structure for non-minor-closed classesJournal of Combinatorial Theory, Series B10.1016/j.jctb.2023.03.004162(34-67)Online publication date: Sep-2023
https://doi.org/10.1016/j.jctb.2023.03.004
Liu CWood D(2023)Clustered coloring of graphs with bounded layered treewidth and bounded degreeEuropean Journal of Combinatorics10.1016/j.ejc.2023.103730(103730)Online publication date: May-2023
https://doi.org/10.1016/j.ejc.2023.103730
Sone KSuzuki Y(2023)Optimal 1-planar multigraphsDiscrete Mathematics10.1016/j.disc.2023.113553346:10Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1016/j.disc.2023.113553
Angelini PBekos MDa Lozzo GGronemann MMontecchiani FTappini A(2023)Recognizing Map Graphs of Bounded TreewidthAlgorithmica10.1007/s00453-023-01180-686:2(613-637)Online publication date: 27-Oct-2023
https://doi.org/10.1007/s00453-023-01180-6
Kim JKim MKwon O(2022)Rainbow independent sets on dense graph classesDiscrete Applied Mathematics10.1016/j.dam.2021.04.007312:C(45-51)Online publication date: 15-May-2022
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de Berg MKisfaludi-Bak SMonemizadeh MTheocharous L(2022)Clique-Based Separators for Geometric Intersection GraphsAlgorithmica10.1007/s00453-022-01041-885:6(1652-1678)Online publication date: 15-Oct-2022
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Huynh TWood D(2021)Tree densities in sparse graph classesCanadian Journal of Mathematics10.4153/S0008414X21000316(1-20)Online publication date: 29-Jun-2021
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