, Volume 3, Issue 3, pp 243–251 | Cite as

Variations on the Roy-Gallai theorem

  • Dominique de Werra
  • Pierre Hansen


A generalization of the Roy-Gallai Theorem on the chromatic number of a graph is derived which is also an extension of several other results of Berge and of Li. A simple inductive proof is given which provides a direct way of deriving the Theorem of Li. We also show that some classical results valid for optimal colorings cannot be transposed to suboptimal colorings. We finally investigate some elementary properties which are also valid in suboptimal colorings.


Graph coloring chromatic number longest path panchromatic chains stable sets 


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Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Institut de MathématiquesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.GERAD and Département des Méthodes Quantitatives de GestionEcole des Hautes Etudes CommercialesMontréalCanada

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