News about Semiantichains and Unichain Coverings
نویسندگان
چکیده
We study a min-max relation conjectured by Saks and West: For any two posets P and Q the size of a maximum semiantichain and the size of a minimum unichain covering in the product P ×Q are equal. For positive we state conditions on P and Q that imply the min-max relation. However, we also have an example showing that in general the min-max relation is false. This disproves the Saks-West conjecture.
منابع مشابه
Duality for Semiantichains and Unichain Coverings in Products of Special Posets
Saks and West conjectured that for every product of partial orders, the maximum size of a semiantichain equals the minimum number of unichains needed to cover the product. We prove the case where both factors have width 2. We also use the characterization of product graphs that are perfect to prove other special cases, including the case where both factors have height 2. Finally, we make some o...
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We study a min-max relation conjectured by Saks and West: For any two posets P and Q the size of a maximum semiantichain and the size of a minimum unichain covering in the product P ×Q are equal. For positive we state conditions on P and Q that imply the min-max relation. Based on these conditions we identify some new families of posets where the conjecture holds and get easy proofs for several...
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