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West, Douglas B. Ramamurthi, Radhika 2015-09-28T15:19:32Z 2015-09-28T15:19:32Z 10000-01-01 2001 2001 An r-edge-coloring of Kn is (r, m)-splittable if V (Kn) can then be r-colored to avoid totally monochromatic m-cliques (introduced by Erdo&huml;s and Gyarfas. We interpret such colorings using a two-round game against an adversary; this relates splittable colorings to classical Ramsey numbers. Let fr(m) be the least n such that some r-edge-coloring of K n is not (r, m)-splittable. Combinatorial designs yield fr(m) ≤ O(r2m2). Extending ideas of Erdo&huml;s and Gyarfas yields f r(m) ≥ min{O(rm 2), O(r2m)}. Similar bounds hold for a generalization to hypergraphs. Made available in DSpace on 2015-09-28T15:19:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023179.pdf: 5443713 bytes, checksum: bf79f01a8f462607312b8b1717ae41ec (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88068 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 103 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86787 (MiAaPQ)AAI3023179 eng Mathematics Coloring Problems on Graphs and Hypergraphs text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.