On a Question of Sós About 3-Uniform Friendship Hypergraphs
نویسندگان
چکیده
The well-known Friendship Theorem states that ifG is a graph in which every pair of vertices has exactly one common neighbor, then G has a single vertex joined to all others (a “universal friend”). V. Sós defined an analogous friendship property for 3-uniformhypergraphs, andgave a construction satisfying the friendshipproperty that has auniversal friend.Wepresent new 3-uniformhypergraphs on 8, 16, and 32 vertices that satisfy the friendship propertywithout containingauniversal friend.Wealsoprove that ifn ≤ 10andn = 8, then there areno friendship hypergraphs on n vertices without a universal friend. These results were obtained by computer search using integer programming. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 253–261, 2008
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