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The Growth of Infinite Graphs: Boundedness and Finite Spreading

Published online by Cambridge University Press:  12 September 2008

Reinhard Diestel  and
Imre Leader
Reinhard Diestel
Affiliation:
Faculty of Mathematics (SFB 343), Bielefeld University, D-4800 Bielefeld, Germany
Imre Leader
Affiliation:
Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, England
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Abstract

An infinite graph is called bounded if for every labelling of its vertices with natural numbers there exists a sequence of natural numbers which eventually exceeds the labelling along any ray in the graph. Thomassen has conjectured that a countable graph is bounded if and only if its edges can be oriented, possibly both ways, so that every vertex has finite out-degree and every ray has a forward oriented tail. We present a counterexample to this conjecture.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 51 - 55
Copyright
Copyright © Cambridge University Press 1994

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References

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