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A condition for the three colourability of planar locally path graphs

  • Algorithms
  • Conference paper
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Book cover Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1026))

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Abstract

A graph G is said to be locally path if for every vertex the subgraph induced by its neighbours is a path. Planar locally path graphs are a natural generalization of maximal outerplanar graphs. We show that they have a recursive construction which generalizes that of maximal outerplanar graphs. Using this characterization we obatin a ’local’ condition for the three colourability of planar locally path graphs. As a corollary, we show that maximal planar graphs are three colourable iff every vertex has even degree. We also derive a structural property of maximal planar graphs.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, 400076, Bombay

    Ajit A. Diwan & N. Usharani

Authors
  1. Ajit A. Diwan
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  2. N. Usharani
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Editor information

P. S. Thiagarajan

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© 1995 Springer-Verlag Berlin Heidelberg

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Diwan, A.A., Usharani, N. (1995). A condition for the three colourability of planar locally path graphs. In: Thiagarajan, P.S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1995. Lecture Notes in Computer Science, vol 1026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60692-0_40

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  • DOI: https://doi.org/10.1007/3-540-60692-0_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60692-5

  • Online ISBN: 978-3-540-49263-4

  • eBook Packages: Springer Book Archive

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