Extending bicolorings 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.

We replace the old version "Extended colorings for $BSTS(2v+1)$"; the related appendix is arxiv:1308.4793. To appear in Applicable Analysis and Discrete Mathematics