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A condition for the three colourability of planar locally path graphs

  • Ajit A. Diwan
  • N. Usharani
Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1026)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Ajit A. Diwan
    • 1
  • N. Usharani
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyBombay

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