Abstract
It is shown that a pairwise balanced design onn points in which each block is of size at leastn 1/2 −c can be embedded in a projective plane of ordern+i for somei≦c + 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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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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DOI: https://doi.org/10.1007/BF02579251