On the Block Coloring of Steiner Triple Systems

Abstract

A {\it Steiner triple system} of order $v$,
STS($v$), is an ordered pair $S=(V,B)$, where $V$ is a set of size
$v$ and $B$ is a collection of triples of $V$ such that every pair
of $V$ is contained in exactly one triple of $B$. A {\it $k$-block
coloring} is a partitioning of the set $B$ into $k$ color classes
such that every two blocks in one color class do not intersect. In this paper, it is proved that for every
$k$-block colorable STS($v$) and $l$-block colorable STS($w$), there
exists a $(k+lv)$-block colorable STS($vw$) obtained from an introduced construction. Moreover, it is shown
that
for every $k$-block colorable   STS($v$), every
STS($2v+1$) obtained from the well-known construction is
$(k+v)$-block colorable.