TY - JOUR

T1 - Transversals in uniform hypergraphs with property (p,2)

AU - V. Kostochka, Alexandr

N1 - Funding Information:
∗ Th is work was partially supported by th e grant 99-01-00581 of th e Russian Foundation for Fundamental Research and th e Dutch –Russian Grant NWO-047-008-006.

PY - 2002

Y1 - 2002

N2 - Let f(r,p,t) (p > t ≥ 1, r ≥ 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs H possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f (r,p,2) for p=3, 4, 5, 6 were found in [1] and hounds on f (r, 7, 2) are given in [3]. Here we prove that f (r,p,2) ≤ 1.3 r/p0.5-o(p0.5) for large p and huge r.

AB - Let f(r,p,t) (p > t ≥ 1, r ≥ 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs H possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f (r,p,2) for p=3, 4, 5, 6 were found in [1] and hounds on f (r, 7, 2) are given in [3]. Here we prove that f (r,p,2) ≤ 1.3 r/p0.5-o(p0.5) for large p and huge r.

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U2 - 10.1007/s004930200013

DO - 10.1007/s004930200013

M3 - Article

AN - SCOPUS:0036332451

SN - 0209-9683

VL - 22

SP - 275

EP - 285

JO - Combinatorica

JF - Combinatorica

IS - 2

ER -