Monotone paths in ordered graphs

Combinatorica volume 2, pages193–201(1982)Cite this 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 inf ⫋V inf ⫋V fin ⫋E fin. Finally we consider labellings by positive integers and characterize the class corresponding toV inf.

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Author information

Affiliations

  1. Mathematical Institute of the Czechoslovak Academy of Sciences, Žitná 28, 11567, Praha I, Czechoslovakia

    Vladimír Müller

  2. Department of Mathematics, Faculty of Nuclear Engineering, Husova 5, 11000, Praha I, Czechoslovakia

    Vojtěch Rödl

Authors
  1. Vladimír Müller
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  2. Vojtěch Rödl
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Müller, V., Rödl, V. Monotone paths in ordered graphs. Combinatorica 2, 193–201 (1982). https://doi.org/10.1007/BF02579318

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AMS subject classification (1980)

  • 05 C 55
  • 05 C 38