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Coloring Ordered Sets to Avoid Monochromatic Maximal Chains

Published online by Cambridge University Press:  20 November 2018

D. Duffus ,
V. Rodl ,
N. Sauer  and
R. Woodrow
D. Duffus
Affiliation:
Mathematics and Computer Science, Emory University, Atlanta, Georgia, USA 30322
V. Rodl
Affiliation:
Mathematics and Computer Science, Emory University, Atlanta, Georgia, USA 30322
N. Sauer
Affiliation:
Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4
R. Woodrow
Affiliation:
Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4
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Abstract

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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.

Keywords

06A10(Partially) ordered setmaximal chain
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 91 - 103
Copyright
Copyright © Canadian Mathematical Society 1991

References

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