Appendix of Extending Bicoloring for Steiner Triple Systems

Abstract

We initiate the study of extended bicolorings of Steiner triple systems (STS) which start with a $k$-bicoloring of an STS($v$) and end up with a $k$-bicoloring of an STS($2v+1$) obtained by a doubling construction, using only the original colors used in coloring the subsystem STS($v$). By producing many such extended bicolorings, we obtain several infinite classes of orders for which there exist STSs with different lower and upper chromatic number.

In this appendix we list all the factorizations $\cal F$ which characterize all the extended bicolorings shown in the paper "Extending Bicoloring for Steiner Triple Systems"