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=&...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
Università degli Studi di Catania
1995-11-01
|
Series: | Le Matematiche |
Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/508 |
id |
doaj-71e5d98debc841c2a7fa0ffbde699c7d |
---|---|
record_format |
Article |
spelling |
doaj-71e5d98debc841c2a7fa0ffbde699c7d2020-11-25T03:40:15ZengUniversità 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 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lorenzo Milazzo |
spellingShingle |
Lorenzo Milazzo On upper chromatic number for SQS(10) and SQS(16) Le Matematiche |
author_facet |
Lorenzo Milazzo |
author_sort |
Lorenzo Milazzo |
title |
On upper chromatic number for SQS(10) and SQS(16) |
title_short |
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_sort |
on upper chromatic number for sqs(10) and sqs(16) |
publisher |
Università degli Studi di Catania |
series |
Le Matematiche |
issn |
0373-3505 2037-5298 |
publishDate |
1995-11-01 |
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. |
url |
http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/508 |
work_keys_str_mv |
AT lorenzomilazzo onupperchromaticnumberforsqs10andsqs16 |
_version_ |
1724535259671822336 |