Israel Journal of Mathematics

, Volume 39, Issue 1–2, pp 145–154

The road-colouring problem

  • G. L. O’brien
Article

Abstract

LetG be a finite directed graph which is irreducible and aperiodic. Assume each vertex ofG leads to at least two other vertices, and assumeG has a cycle of prime length which is a proper subset ofG. Then there exist two functionsr:GG andb:GG such that ifr(x)=y andb(x)=z thenxy andxz inG andyz and such that some composition ofr’s andb’s is a constant function.

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References

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    R. L. Adler, L. W. Goodwyn and B. Weiss,Equivalence of topological Markov shifts, Israel J. Math.27 (1977), 49–63.MATHCrossRefMathSciNetGoogle Scholar
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    J. W. Moon,Counting Labelled Trees, Canadian Mathematical Congress Monograph No.1, 1970.Google Scholar
  3. 3.
    G. L. O’Brien,Zero-inducing functions on finite abelian groups, to appear (1981).Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1981

Authors and Affiliations

  • G. L. O’brien
    • 1
  1. 1.Department of MathematicsYork UniversityDownsviewCanada

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