Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s
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 c...
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2011-06-01
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| Series: | Computer Science Journal of Moldova |
| Online Access: | http://www.math.md/files/csjm/v19-n1/v19-n1-(pp29-37).pdf |
| Summary: | 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 $BSTS (15)$. |
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| ISSN: | 1561-4042 |