Graphs and Combinatorics

, Volume 16, Issue 4, pp 389–398 | Cite as

Colour Number, Capacity, and Perfectness of Directed Graphs

  • Emanuela Fachini
  • János Körner

Abstract.

We introduce a new concept of chromatic number for directed graphs, called the colour number and use it to upper bound the transitive clique number and the Sperner capacity of arbitrary directed graphs. Our results represent a common generalization of previous bounds of Alon and the second author and lead to a concept of perfectness for directed graphs.

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Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Emanuela Fachini
    • 1
  • János Körner
    • 2
  1. 1.Department of Computer Science, La Sapienza University of Roma, via Salaria 113, 00198 Roma, Italy e-mail: fachini@dsi.uniromal.itIT
  2. 2.Department of Computer Science, La Sapienza University of Roma, via Salaria 113, 00198 Roma, Italy e-mail: korner@dsi.uniroma1.itIT

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