The road-colouring problem
- G. L. O’brien
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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:G →G andb:G →G such that ifr(x)=y andb(x)=z thenx →y andx →z inG andy ≠z and such that some composition ofr’s andb’s is a constant function.
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- J. W. Moon,Counting Labelled Trees, Canadian Mathematical Congress Monograph No.1, 1970.
- G. L. O’Brien,Zero-inducing functions on finite abelian groups, to appear (1981).
- The road-colouring problem
Israel Journal of Mathematics
Volume 39, Issue 1-2 , pp 145-154
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- G. L. O’brien (1)
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- 1. Department of Mathematics, York University, M3J 1P3, Downsview, Ontario, Canada