Lower and upper chromatic numbers for BSTSs(2h - 1)

Abstract

In [Discrete Math. 174, (1997) 247-259] an infinite class of STSs(2h - 1) was found with the upper chromatic number not(χ)=h. We prove that in this class, for all STSs(2h - 1) with h<10, the lower chromatic number coincides with the upper chromatic number, i.e. χ=not(χ)=h and moreover, there exists a infinite sub-class of STSs with χ=not(χ)=h for any value of h.