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On the Turán Number of Triple Systems

✍ Scribed by Dhruv Mubayi; Vojtêch Rödl

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
176 KB
Volume
100
Category
Article
ISSN
0097-3165

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✦ Synopsis

For a family of r-graphs F; the Tur! a an number exðn; FÞ is the maximum number of edges in an n vertex r-graph that does not contain any member of F: The Tur! a an density

When F is an r-graph, pðFÞ=0; and r > 2; determining pðFÞ is a notoriously hard problem, even for very simple r-graphs F: For example, when r ¼ 3; the value of pðFÞ is known for very few ð510Þ irreducible r-graphs. Building upon a method developed recently by de Caen and F . u uredi (J. Combin. Theory Ser. B 78 (2000), 274-276), we determine the Tur! a an densities of several 3-graphs that were not previously known. Using this method, we also give a new proof of a result of Frankl and F . u uredi (Combinatorica 3 (1983), 341-349) that pðHÞ ¼ 2 9 ; where H has edges 123; 124; 345:

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