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West, Douglas B. Prince, Noah B. 2015-09-28T15:20:06Z 2015-09-28T15:20:06Z 10000-01-01 2008 2008 Our final problem is one in graph representations. We develop a lemma on traces of hypergraphs, extending results of Balogh and Bollobas. We then use this lemma, along with probabilistic methods, to show that for every positive integer k, almost every graph has no k-minimum-difference-representation. This answers a question of Boros, Gurvich, and Meshulam. Made available in DSpace on 2015-09-28T15:20:06Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3314867.pdf: 1406087 bytes, checksum: 4e133118f4ee58378072665de2ed1fde (MD5) Previous issue date: 2008 Embargo set by: Seth Robbins for item 88183 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 102 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. http://hdl.handle.net/2142/86902 (MiAaPQ)AAI3314867 eng Mathematics Delta-System Methods in Contemporary Graph Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.