On upper chromatic number for SQS(10) and SQS(16)
A mixed hypergraph is characterized by the fact that it possesses anti-edges as well as edges. In a colouring of a mixed hypergraph, every anti-edge has at least two vertices of the same colour and every edge has at least two vertices coloured differently. The upper chromatic number <span style=&...
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
1995-11-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/508 |
| _version_ | 1811325428045971456 |
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| author | Lorenzo Milazzo |
| author_facet | Lorenzo Milazzo |
| author_sort | Lorenzo Milazzo |
| collection | DOAJ |
| description | A mixed hypergraph is characterized by the fact that it possesses anti-edges as well as edges. In a colouring of a mixed hypergraph, every anti-edge has at least two vertices of the same colour and every edge has at least two vertices coloured differently. The upper chromatic number <span style="text-decoration: underline;">X</span> is the maximal number of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph and upper chromatic number are applied to STS and SQS. In fact it is possible to consider a Steiner system as a mixed hypergraph when all the blocks are anti-edges (Co-STSs, Co-SQSs) or at the same time edges and anti-edges (BSTSs, BSQSs). In this paper the necessary conditions in order to colour Co-STSs, BSTSs and Co-SQSs, BSQSs are given and the values of upper chromatic number for Co-SQS(10), BSQS(10) and for BSQSs(16), obtained from a doubling construction, are determined. |
| first_indexed | 2024-04-13T14:32:50Z |
| format | Article |
| id | doaj.art-71e5d98debc841c2a7fa0ffbde699c7d |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-04-13T14:32:50Z |
| publishDate | 1995-11-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-71e5d98debc841c2a7fa0ffbde699c7d2022-12-22T02:43:07ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981995-11-01501179193476On upper chromatic number for SQS(10) and SQS(16)Lorenzo MilazzoA mixed hypergraph is characterized by the fact that it possesses anti-edges as well as edges. In a colouring of a mixed hypergraph, every anti-edge has at least two vertices of the same colour and every edge has at least two vertices coloured differently. The upper chromatic number <span style="text-decoration: underline;">X</span> is the maximal number of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph and upper chromatic number are applied to STS and SQS. In fact it is possible to consider a Steiner system as a mixed hypergraph when all the blocks are anti-edges (Co-STSs, Co-SQSs) or at the same time edges and anti-edges (BSTSs, BSQSs). In this paper the necessary conditions in order to colour Co-STSs, BSTSs and Co-SQSs, BSQSs are given and the values of upper chromatic number for Co-SQS(10), BSQS(10) and for BSQSs(16), obtained from a doubling construction, are determined.http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/508 |
| spellingShingle | Lorenzo Milazzo On upper chromatic number for SQS(10) and SQS(16) Le Matematiche |
| title | On upper chromatic number for SQS(10) and SQS(16) |
| title_full | On upper chromatic number for SQS(10) and SQS(16) |
| title_fullStr | On upper chromatic number for SQS(10) and SQS(16) |
| title_full_unstemmed | On upper chromatic number for SQS(10) and SQS(16) |
| title_short | On upper chromatic number for SQS(10) and SQS(16) |
| title_sort | on upper chromatic number for sqs 10 and sqs 16 |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/508 |
| work_keys_str_mv | AT lorenzomilazzo onupperchromaticnumberforsqs10andsqs16 |