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Coloring Ordered Sets to Avoid Monochromatic Maximal Chains
Published online by Cambridge University Press: 20 November 2018
Abstract
This paper is devoted to settling the following problem on (infinite, partially) ordered sets: Is there always a partition (2-coloring) of an ordered set X so that all nontrivial maximal chains of X meet both classes (receive both colors)? We show this is true for all countable ordered sets and provide counterexamples of cardinality N3. Variants of the problem are also considered and open problems specified.
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- Copyright © Canadian Mathematical Society 1991
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