𝔖 Bobbio Scriptorium
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Chain partitions of ordered sets

✍ Scribed by Zbigniew Lonc

Book ID
105075175
Publisher
Springer Netherlands
Year
1994
Tongue
English
Weight
507 KB
Volume
11
Category
Article
ISSN
0167-8094

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We analyze the on-line chain partitioning problem as a two-person game. One person builds an order one point at a time. The other person responds by making an irrevocable assignment of the new point to a chain of a chain partition. Kierstead gave a strategy showing that width k orders can be on-line

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It is shown that if a chain complete ordered set does not have k+ 1 pairwise disjoint maximal chains for some finite k, then the minimum size of a cutset is equal to the maximum size of a collection of pairwise disjoint maximal chains. This answers a question of Pouzet and Zaguia.