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Combinatorica

, Volume 2, Issue 2, pp 193–201 | Cite as

Monotone paths in ordered graphs

  • Vladimír Müller
  • Vojtěch Rödl
Article

Abstract

LetV fin andE fin resp. denote the classes of graphsG with the property that no matter how we label the vertices (edges, resp.) ofG by members of a linearly ordered set, there will exist paths of arbitrary finite lengths with monotonically increasing labels. The classesV inf andE inf are defined similarly by requiring the existence of an infinite path with increasing labels. We proveE infV infV finE fin. Finally we consider labellings by positive integers and characterize the class corresponding toV inf.

AMS subject classification (1980)

05 C 55 05 C 38 

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Copyright information

© Akadémiai Kiadó 1982

Authors and Affiliations

  • Vladimír Müller
    • 1
  • Vojtěch Rödl
    • 2
  1. 1.Mathematical Institute of the Czechoslovak Academy of SciencesPraha ICzechoslovakia
  2. 2.Department of MathematicsFaculty of Nuclear EngineeringPraha ICzechoslovakia

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