Zoltán Füredi

Zoltán Füredi (Budapest, Hungary, 21 May 1954) is a Hungarian mathematician, working in combinatorics, mainly in discrete geometry and extremal combinatorics. He was a student of Gyula O. H. Katona. He is a corresponding member of the Hungarian Academy of Sciences (2004). He is a research professor of the Rényi Mathematical Institute of the Hungarian Academy of Sciences, and a professor at the University of Illinois Urbana-Champaign (UIUC).

Füredi received his Candidate of Sciences degree in mathematics in 1981 from the Hungarian Academy of Sciences.^[1]

Some results

• In infinitely many cases he determined the maximum number of edges in a graph with no C₄.^[2]
• With Paul Erdős he proved that for some c>1, there are c^d points in d-dimensional space such that all triangles formed from those points are acute.
• With Imre Bárány he proved that no polynomial time algorithm determines the volume of convex bodies in dimension d within a multiplicative error d^d.
• He proved that there are at most ${\displaystyle O(n\log n)}$  unit distances in a convex n-gon.^[3]
• In a paper written with coauthors he solved the Hungarian lottery problem.^[4]
• With Ilona Palásti he found the best known lower bounds on the orchard-planting problem of finding sets of points with many 3-point lines.^[5]
• He proved an upper bound on the ratio between the fractional matching number and the matching number in a hypergraph.^[6]

References

1. Zoltán Füredi at the Mathematics Genealogy Project
2. Füredi, Zoltán (1983). "Graphs without quadrilaterals". Journal of Combinatorial Theory, Series B. Elsevier BV. 34 (2): 187–190. doi:10.1016/0095-8956(83)90018-7. ISSN 0095-8956.
3. Z. Füredi (1990). "The maximum number of unit distances in a convex n-gon". Journal of Combinatorial Theory. Series A. 55 (2): 316–320. doi:10.1016/0097-3165(90)90074-7.
4. Z. Füredi, G. J. Székely, and Z. Zubor (1996). "On the lottery problem". Journal of Combinatorial Designs. 4 (1): 5–10. doi:10.1002/(sici)1520-6610(1996)4:1<5::aid-jcd2>3.3.co;2-w.{{cite journal}}: CS1 maint: multiple names: authors list (link) [1] Reprint
5. Füredi, Z.; Palásti, I. (1984). "Arrangements of lines with a large number of triangles". Proceedings of the American Mathematical Society. 92 (4): 561–566. doi:10.1090/S0002-9939-1984-0760946-2. JSTOR 2045427..
6. Füredi, Zoltán (1 June 1981). "Maximum degree and fractional matchings in uniform hypergraphs". Combinatorica. 1 (2): 155–162. doi:10.1007/BF02579271. ISSN 1439-6912. S2CID 10530732.

External links

• Füredi's UIUC home page