A note on monotone paths in labeled graphs

Abstract

We characterize countable graphs with the property that every one-to-one labeling of edges by positive integers admits a monotone path.

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References

  1. [1]

    V. Müller andV. Rödl, Monotone paths in ordered graphs,Combinatorica,2 (1982), 193–201.

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Reiterman, J. A note on monotone paths in labeled graphs. Combinatorica 9, 231–232 (1989). https://doi.org/10.1007/BF02124684

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AMS subject classification (1980)

  • 05 C 38