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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Main Authors: Jeremy Mathews, Brett Tolbert
Format: Article
Language:English
Published: Vladimir Andrunachievici Institute of Mathematics and Computer Science 2010-07-01
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).
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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
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