Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s - Jeremy Mathews (Computer Science Journal of Moldova, 2011)
A Bi-Steiner Triple System ($BSTS$) is a Steiner Triple System with vertices colored in such a way that the vertices of each block receive precisely two colors. When we consider all $BSTS (15)$s as mixed hypergraphs, we find that some are colorable while others are uncolorable. The criterion for colorability for a $BSTS (15)$ by Rosa is containing $BSTS (7)$ as a subsysytem. Of the 80 non-isomorphic $BSTS (15)$s, only 23 meet this criterion and are therefore colorable. The other 57 are uncolorable. The question arose of finding maximal induced colorable subhypergraphs of these 57 uncolorable $BSTS (15)$s. This paper gives feasible partitions of maximal induced colorable subhypergraphs of each uncolorable $BSTS (15)$.