Two Questions of Erdos on Hypergraphs above the Turan Threshold
2014 (English)In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 76, no 2, 101-105 p.Article in journal (Refereed) Published
For ordinary graphs it is known that any graph G with more edges than the Turan number of Ks must contain several copies of Ks, and a copy of Ks+1-, the complete graph on s+1 vertices with one missing edge. Erdos asked if the same result is true for Ks3, the complete 3-uniform hypergraph on s vertices. In this note, we show that for small values of n, the number of vertices in G, the answer is negative for s=4. For the second property, that of containing a Ks+13-, we show that for s=4 the answer is negative for all large n as well, by proving that the Turan density of K53- is greater than that of K43.
Place, publisher, year, edition, pages
2014. Vol. 76, no 2, 101-105 p.
turan problem, hypergraphs
IdentifiersURN: urn:nbn:se:umu:diva-88377DOI: 10.1002/jgt.21752ISI: 000333643600002OAI: oai:DiVA.org:umu-88377DiVA: diva2:715508