On the Block Coloring of Steiner Triple Systems

A steiner triple system of order v, sts(v), is an orderedpair s = (v,b), where v is a set of size v and b is a collection oftriples of v such that every pair of v is contained in exactly one tripleof b. a k-block coloring is a partitioning of the set b into k color classessuch that every two blocks in one color class do not intersect. in thispaper, we introduce a construction and use it to show that for everyk-block colorable sts(v) and l-block colorable sts(w), there exists a(k+lv)-block colorable sts(vw). moreover, it is shown that for every kblockcolorable sts(v), every sts(2v+1) obtained from the well-knownconstruction is (k + v)-block colorable.