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Israel Journal of Mathematics

, Volume 39, Issue 1–2, pp 145–154 | Cite as

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.

Keywords

Constant Function Distinct Element Proper Subset Finite Abelian Group Prime Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. L. Adler, L. W. Goodwyn and B. Weiss,Equivalence of topological Markov shifts, Israel J. Math.27 (1977), 49–63.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    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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