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 subsystem. 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).
Troy, AL 36082
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