**Authors:** Jeremy Mathews, Brett Tolbert

### 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

E-mail: ,

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