{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86981"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86981","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Extremal Problems in Combinatorics: Covering and Coloring Problems","abstract":"The Ramsey-type coloring problems we consider include generalized Ramsey and generalized Anti-Ramsey problems. Namely, what is the minimal (or maximal) number of colors on the edges of a graph such that every subgraph isomorphic to some fixed graph uses at most q2 and at least q1 colors on its edges. Thus we generalize the results of Erdős, Gyarfas, Simonovits and Sos and solve some of their old open problems.","abstract_html":"The Ramsey-type coloring problems we consider include generalized Ramsey and generalized Anti-Ramsey problems. Namely, what is the minimal (or maximal) number of colors on the edges of a graph such that every subgraph isomorphic to some fixed graph uses at most q2 and at least q1 colors on its edges. 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