Summary
A p-representation of the complete graph Κ n, n is a collection of sets {S 1, S 2, …, S 2n } such that |S i ∩ S j | ≥ p if and only if i ≤ n < j. Let υ p (Κ n, n ) be the smallest cardinality of ∪S i . Using the Frankl-Rödl theorem about almost perfect matchings in uncrowded hypergraphs we prove the following conjecture of Chung and West. For fixed p while n → ∞ we have υ p (Κ n, n ) = (1 + º(1))n 2/p. Several problems remain open.
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© 1997 Springer-Verlag Berlin Heidelberg
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Füredi, Z. (1997). Intersection Representations of the Complete Bipartite Graph. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös II. Algorithms and Combinatorics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60406-5_9
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DOI: https://doi.org/10.1007/978-3-642-60406-5_9
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