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 |
| _version_ | 1811303346992054272 |
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| author | Jeremy Mathews |
| author_facet | Jeremy Mathews |
| author_sort | Jeremy Mathews |
| collection | DOAJ |
| description | 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 $BSTS (15)$. |
| first_indexed | 2024-04-13T07:45:18Z |
| format | Article |
| id | doaj.art-f9b6ab65e4774c3b8bbfe7e94598efa4 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-13T07:45:18Z |
| publishDate | 2011-06-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-f9b6ab65e4774c3b8bbfe7e94598efa42022-12-22T02:55:42ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422011-06-01191(55)2937Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)sJeremy Mathews0Troy University, Troy, AL 36082A 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 $BSTS (15)$.http://www.math.md/files/csjm/v19-n1/v19-n1-(pp29-37).pdf |
| spellingShingle | Jeremy Mathews Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s Computer Science Journal of Moldova |
| title | Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s |
| title_full | Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s |
| title_fullStr | Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s |
| title_full_unstemmed | Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s |
| title_short | Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s |
| title_sort | maximal induced colorable subhypergraphs of all uncolorable bsts 15 s |
| url | http://www.math.md/files/csjm/v19-n1/v19-n1-(pp29-37).pdf |
| work_keys_str_mv | AT jeremymathews maximalinducedcolorablesubhypergraphsofalluncolorablebsts15s |