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Description
Title: | Some Extremal Problems on Graphs and Partial Orders |
Author(s): | Liu, Qi |
Doctoral Committee Chair(s): | West, Douglas B. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | A unichain in a product poset P x Q is a chain in which the value of one coordinate is fixed. A semiantichain in P x Q is a family S such that (u, v) < ( u', v') for two elements of S only if u < u' and v < v' . 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 an observation about the case where both factors have dimension 2. |
Issue Date: | 2007 |
Type: | Text |
Language: | English |
Description: | 81 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. |
URI: | http://hdl.handle.net/2142/86887 |
Other Identifier(s): | (MiAaPQ)AAI3290301 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2007 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois