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West, Douglas B. Liu, Qi 2015-09-28T15:20:00Z 2015-09-28T15:20:00Z 10000-01-01 2007 2007 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. Made available in DSpace on 2015-09-28T15:20:00Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290301.pdf: 2487832 bytes, checksum: 53d6aca1638323998709dab480a3f627 (MD5) Previous issue date: 2007 Embargo set by: Seth Robbins for item 88168 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 81 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. http://hdl.handle.net/2142/86887 (MiAaPQ)AAI3290301 eng Mathematics Some Extremal Problems on Graphs and Partial Orders text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.