On a problem of Erdős and Larson

Abstract

It is shown that a pairwise balanced design onn points in which each block is of size at leastn 1/2c can be embedded in a projective plane of ordern+i for someic + 2 ifn is sufficiently large. Among other things this implies that if the projective plane conjecture is true, the conjecture of Erdős and Larson will not be true.

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References

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    N. G. De Bruijn andP. Erdős, On a Combinatorial Problem,Nederl. Akad. Wet 51 (1948), 1277–1279.

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The paper was written during a visit of the second author to Mehta Research Institute, Allahabad.

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Shrikhande, S.S., Singhi, N.M. On a problem of Erdős and Larson. Combinatorica 5, 351–358 (1985). https://doi.org/10.1007/BF02579251

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AMS subject classification (1980)

  • 05 B 30