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t-expansive andt-wise intersecting hypergraphs

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Abstract

We give a hypergraph generalization of Gallai's theorem about factor-critical graphs. This result can be used to determineτ *(r, t) forr < 3t/2, whereτ *(r, t) denotes the maximum value of the fractional covering numbers oft-wise intersecting hypergraphs of rankr.

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References

  1. Alon, N., Füredi, Z.: On the kernel of intersecting families.

  2. Bang, C., Sharp, H., Winkler, P.: On coverings of a finite set: depth and subcovers. Period. Math. Hung.15, 51–60 (1984)

    Google Scholar 

  3. Brace, A., Daykin, D.E.: Cover theorems for finite sets I–III. Bull. Aust. Math. Soc.5, 197–202 (1971),6, 19–24 (1972),6, 417–433 (1972)

    Google Scholar 

  4. Daykin, D.E.: Problem E 2654. Amer. Math. Mon.84, 386 (1977). Minimum subcover of a cover of a finite set (Problem E 2654). Amer. Math. Mon.85, 766 (1978)

    Google Scholar 

  5. Daykin, D.E., Frankl, P.: Sets of finite sets satisfying union conditions. Mathematica29, 128–134 (1982)

    Google Scholar 

  6. Edmonds, J.: Paths, trees, and flowers. Canad. J. Math.17, 449–467 (1965)

    Google Scholar 

  7. Erdös, P., Lovász, L.: Problems and results in 3-chromatic hypergraphs and some related questions. In: Infinite and Finite Sets. Colloq. Math. Soc. János Bolyai10, 609–627 (1975)

    Google Scholar 

  8. Erdös, P., Rado, R.: Intersection theorems for systems of sets. J. London Math. Soc.35, 85–90 (1960)

    Google Scholar 

  9. Frankl, P., Füredi, Z.: Finite projective spaces and intersecting hypergraphs. Combinatorica (to appear)

  10. Füredi, Z.: Maximum degree and fractional matchings in uniform hypergraphs. Combinatorica1, 155–162 (1981)

    Google Scholar 

  11. Gallai, T.: Neuer Beweis eines Tutte'shen Satzes. MTA Math. Kut. Int. Közl.8, 135–139 (1963)

    Google Scholar 

  12. Hanson, D., Toft, B.: On the maximum number of vertices inn-uniform cliques. Ars Comb.16-A, 205–216 (1983)

    Google Scholar 

  13. Lovász, L.: Combinatorial Problems and Exercises. Budapest: Akadémiai Kiadó/Amsterdam: North-Holland 1979

    Google Scholar 

  14. Lovász, L.: Doctoral Thesis. Szeged 1977. Also see: On minimax theorems of combinatorics (in Hungarian). Mat. Lapok26, 209–264 (1975)

    Google Scholar 

  15. Lovász, L.: Minimax theorems for hypergraphs. In: Hypergraph Seminar 1972, Lecture Notes in Mathematics 411, pp 111–126. Berlin-Heidelberg-New York: Springer-Verlag 1972

    Google Scholar 

  16. Meyer, J.-C.: Quelques problémes concernant les cliques des hypergraphsh-complets etq-partih-complets. In: Hypergraph Seminar 1972, Lecture Notes in Mathematics 411, pp 127–139. Berlin-Heidelberg-New York: Springer-Verlag 1974

    Google Scholar 

  17. Tuza, Z.: Critical hypergraphs and intersecting set-pair systems. J. Comb. Theory (B)39, 134–145 (1985)

    Google Scholar 

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Authors and Affiliations

  1. Math. Inst. Hungarian Acad. Sci., P.O.B. 127, 1364, Budapest, Hungary

    Z. Füredi

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  1. Z. Füredi
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Dedicated to Tibor Gallai

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Füredi, Z. t-expansive andt-wise intersecting hypergraphs. Graphs and Combinatorics 2, 67–80 (1986). https://doi.org/10.1007/BF01788079

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  • DOI: https://doi.org/10.1007/BF01788079

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