{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86904"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86904","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Five Topics in Extremal and Structural Graph Theory","abstract":"The Friendship Theorem states that if G is a graph in which every two vertices have exactly one common neighbor, then G has a dominating vertex. Sos defined an analogous friendship property for 3-uniform hypergraphs, and constructed a family satisfying it. We present additional 3-uniform hypergraphs on 8, 16, and 32 vertices that satisfy this property that were obtained using integer programming. 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Sos defined an analogous friendship property for 3-uniform hypergraphs, and constructed a family satisfying it. We present additional 3-uniform hypergraphs on 8, 16, and 32 vertices that satisfy this property that were obtained using integer programming. No examples outside the family construct by Sos were previously known.","Made available in DSpace on 2015-09-28T15:20:06Z (GMT). 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Sos defined an analogous friendship property for 3-uniform hypergraphs, and constructed a family satisfying it. We present additional 3-uniform hypergraphs on 8, 16, and 32 vertices that satisfy this property that were obtained using integer programming. No examples outside the family construct by Sos were previously known.","Made available in DSpace on 2015-09-28T15:20:06Z (GMT). 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