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On Chordal and Perfect Plane Triangulations

  • Sameera M. Salam
  • Daphna ChackoEmail author
  • Nandini J. Warrier
  • K. Murali Krishnan
  • K. S. Sudeep
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

We investigate a method of decomposing a plane near-triangulation G into a collection of induced component subgraphs which we call the W components of the graph. Each W component is essentially a plane near-triangulation with the property that the neighbourhood of every internal vertex induces a wheel. The problem of checking whether a plane near-triangulation G is chordal (or perfect) is shown to be transformable to the problem of checking whether its W components are chordal (or perfect). Using this decomposition method, we show that a plane near-triangulated graph is chordal if and only if it does not contain an internal vertex whose closed neighbourhood induces a wheel of at least five vertices. Though a simple local characterization for plane perfect near-triangulations is unlikely, we show that there exists a local characterization for perfect W components that does not contain any induced wheel of five vertices.

Keywords

Plane triangulated graphs Plane near-triangulated graphs Chordal graphs Perfect graphs 

Notes

Acknowledgment

We would like to thank Dr. Ajit A Diwan, IIT Bombay and Dr. Jasine Babu, IIT Palakkad for their comments and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sameera M. Salam
    • 1
  • Daphna Chacko
    • 1
    Email author
  • Nandini J. Warrier
    • 1
  • K. Murali Krishnan
    • 1
  • K. S. Sudeep
    • 1
  1. 1.Department of Computer ScienceNational Institute of Technology CalicutKozhikodeIndia

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