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All proper colorings of every colorable BSTS (15)
Authors: Jeremy Mathews, Brett Tolbert
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Abstract
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).Troy University, Troy, AL 36082
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Fulltext
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Contents
- A flexible navigation mechanism for complex data models
- Three models for gene assembly in ciliates: a comparison
- All proper colorings of every colorable BSTS (15)
- Convexity preserving interpolation by splines of arbitrary degree
- Determining best-case and worst-case times of unknown paths in time workflow nets
- Determination of inflexional group using P systems
- Developing a derivatives generator
