Extending bicolorings for Steiner Triple Systems

TL;DR

This paper explores extending bicolorings in Steiner triple systems to larger systems via doubling, revealing infinite classes with varying chromatic numbers.

Contribution

It introduces the concept of extended bicolorings in Steiner triple systems and demonstrates their application in constructing systems with diverse chromatic properties.

Findings

Infinite classes of Steiner triple systems with different chromatic numbers.

Method for extending bicolorings from smaller to larger systems.

New constructions using doubling techniques.

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.