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https://hdl.handle.net/2142/86787
Description
Title
Coloring Problems on Graphs and Hypergraphs
Author(s)
Ramamurthi, Radhika
Issue Date
2001
Doctoral Committee Chair(s)
West, Douglas B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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.
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