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How to Draw Planar Graphs

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Abstruse

A graph is planar if it can be fatigued or embedded in the airplane so that no two edges intersect geometrically except at a vertex to which they are both incident. A plane graph is a planar graph with a stock-still planar embedding in the airplane. A drawing trouble X for a plane graph 1000 asks to determine whether Grand has a drawing D satisfying a prepare P of given properties and to find D if information technology exists. The corresponding trouble for a planar graph G asks to determine whether One thousand has a planar embedding \(\varGamma \) such that \(\varGamma \) has a drawing D satisfying the set P of backdrop and find D if it exists. If every embedding of Thousand has a drawing D satisfying P, then the problem is footling, i.e., the problem for airplane graphs and that for planar graphs are the same. Otherwise, the problem for planar graphs becomes difficult even if an efficient solution of the trouble for a airplane graph exists since a planar graph may accept an exponential number of planar embeddings. Various techniques are found in literature that are used to solve the drawing bug for planar graphs. In this paper nosotros review 3 of the widely used techniques, namely, (i) reduction to planarity testing, (ii) incremental modification and (three) SPQR-tree decomposition.

Keywords

  • Graph drawing
  • Plane graph
  • Planar graph
  • Planarity testing
  • SPQR-tree

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Acknowledgement

Nosotros thank Debajyoti Mondal and Shin-ichi Nakano for their useful comments on the manuscript of this paper.

Author information

Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Reckoner Science and Engineering, People's republic of bangladesh University of Engineering and Applied science (BUET), Dhaka, m, People's republic of bangladesh

    Doc. Saidur Rahman

  2. Department of Computer Scientific discipline and Technology, University of Dhaka, Dhaka, 1000, Bangladesh

    Md. Rezaul Karim

Respective author

Correspondence to Md. Saidur Rahman .

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Rahman, M.Due south., Karim, 1000.R. (2020). Drawing Planar Graphs. In: Rahman, M., Sadakane, Yard., Sung, WK. (eds) WALCOM: Algorithms and Ciphering. WALCOM 2020. Lecture Notes in Computer science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_1

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