Geodesic
Coloring Ordered Sets to Avoid Monochromatic Maximal Chains
Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 91-103

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1992-005-1
Mots-clés : 06A10, (Partially) ordered set, maximal chain 
Duffus, D.; Rodl, V.; Sauer, N.; Woodrow, R. Coloring Ordered Sets to Avoid Monochromatic Maximal Chains. Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 91-103. doi: 10.4153/CJM-1992-005-1
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     title = {Coloring {Ordered} {Sets} to {Avoid} {Monochromatic} {Maximal} {Chains}},
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     pages = {91--103},
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