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Further 6-sparse Steiner triple systems. (English) Zbl 1188.05034
Erdös conjectured that for each $$k\geq 4$$ there exists $$v(k)$$ so that for every admissible $$v>v(k)$$ there exists a Steiner Triple System on $$v$$ points, $$STS(v),$$ which does contains no configuration having $$n$$ blocks on $$n+2$$ points for $$n$$ with $$4\leq n\leq k.$$ Such $$STS(v)$$ is called to be $$k$$-sparse. The existence of $$4$$-sparse systems for all admissible values of $$v,$$ and the existence of $$5$$-sparse systems for almost all admissible values of $$v$$ has been established. In this paper the authors construct a $$6$$-sparse $$STS(v)$$ for $$v=3p,$$ where $$p$$ is sufficiently big prime $$p\equiv 3\pmod {4}$$.

##### MSC:
 05B07 Triple systems
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##### References:
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