All proper colorings of every colorable BSTS(15)
A Steiner System, denoted S(t,k,v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case of a Steiner System where t = 2, k = 3 and v...
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Format: | Article |
Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2010-07-01
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Series: | Computer Science Journal of Moldova |
Online Access: | http://www.math.md/files/csjm/v18-n1/v18-n1-(pp41-53).pdf |
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author | Jeremy Mathews Brett Tolbert |
author_facet | Jeremy Mathews Brett Tolbert |
author_sort | Jeremy Mathews |
collection | DOAJ |
description | A Steiner System, denoted S(t,k,v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case of a Steiner System where t = 2, k = 3 and v = 1 or 3(mod 6) [7]. A Bi-Steiner Triple System, or BSTS, is a Steiner Triple System with the vertices colored in such a way that each block of vertices receives precisely two colors. Out of the 80 BSTS (15)s, only 23 are colorable [1]. In this paper, using a computer program that we wrote, we give a complete description of all proper colorings, all feasible partitions, chromatic polynomial and chromatic spectrum of every colorable BSTS (15). |
first_indexed | 2024-12-10T08:04:47Z |
format | Article |
id | doaj.art-d2431b28b7ae47e5ad49d9ebdac47c42 |
institution | Directory Open Access Journal |
issn | 1561-4042 |
language | English |
last_indexed | 2024-12-10T08:04:47Z |
publishDate | 2010-07-01 |
publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
record_format | Article |
series | Computer Science Journal of Moldova |
spelling | doaj.art-d2431b28b7ae47e5ad49d9ebdac47c422022-12-22T01:56:42ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422010-07-01181(52)4153All proper colorings of every colorable BSTS(15)Jeremy Mathews0Brett Tolbert1Troy University, Troy, AL 36082 Troy University, Troy, AL 36082 A Steiner System, denoted S(t,k,v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case of a Steiner System where t = 2, k = 3 and v = 1 or 3(mod 6) [7]. A Bi-Steiner Triple System, or BSTS, is a Steiner Triple System with the vertices colored in such a way that each block of vertices receives precisely two colors. Out of the 80 BSTS (15)s, only 23 are colorable [1]. In this paper, using a computer program that we wrote, we give a complete description of all proper colorings, all feasible partitions, chromatic polynomial and chromatic spectrum of every colorable BSTS (15).http://www.math.md/files/csjm/v18-n1/v18-n1-(pp41-53).pdf |
spellingShingle | Jeremy Mathews Brett Tolbert All proper colorings of every colorable BSTS(15) Computer Science Journal of Moldova |
title | All proper colorings of every colorable BSTS(15) |
title_full | All proper colorings of every colorable BSTS(15) |
title_fullStr | All proper colorings of every colorable BSTS(15) |
title_full_unstemmed | All proper colorings of every colorable BSTS(15) |
title_short | All proper colorings of every colorable BSTS(15) |
title_sort | all proper colorings of every colorable bsts 15 |
url | http://www.math.md/files/csjm/v18-n1/v18-n1-(pp41-53).pdf |
work_keys_str_mv | AT jeremymathews allpropercoloringsofeverycolorablebsts15 AT bretttolbert allpropercoloringsofeverycolorablebsts15 |