2026-09-20T07:18:32Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/16762 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

West, Douglas B. Kostochka, Alexandr V. West, Douglas B. Jockusch, Carl G., Jr. Vijay, Sujith Milans, Kevin G. 2010-08-20T17:57:12Z 2010-08-20T17:57:12Z 2010-08-20T17:57:12Z 2010-08 We study problems in extremal graph theory with respect to edge-colorings, independent sets, and cycle spectra. In Chapters 2 and 3, we present results in Ramsey theory, where we seek Ramsey host graphs with small maximum degree. In Chapter 4, we study a Ramsey-type problem on edge-labeled trees, where we seek subtrees that have a small number of path-labels. In Chapter 5, we examine parity edge-colorings, which have connections to additive combinatorics and the minimum dimension of a hypercube in which a tree embeds. In Chapter 6, we prove results on the chromatic number of circle graphs with clique number at most 3. The tournament analogue of an independent set is an acyclic set. In Chapter 7, we present results on the size of maximum acyclic sets in k-majority tournaments. In Chapter 8, we prove a lower bound on the size of the cycle spectra of Hamiltonian graphs. Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-07-15T19:06:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Milans_Kevin.pdf: 949867 bytes, checksum: 4c2164e5db50771fcd467e100f4b52a8 (MD5) Made available in DSpace on 2010-08-20T17:57:12Z (GMT). No. of bitstreams: 2 Milans_Kevin.pdf: 949867 bytes, checksum: 4c2164e5db50771fcd467e100f4b52a8 (MD5) license.txt: 4060 bytes, checksum: a5eb72f176eaad29320a4a460ee71718 (MD5) http://hdl.handle.net/2142/16762 en Copyright 2010 Kevin G. Milans Graph Theory Extremal Problems Ramsey Theory Extremal problems on edge-colorings, independent sets, and cycle spectra of graphs Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD