The Spectrum of Non-Polychromatic Equitable Edge Colored Steiner Triple Systems

In [1], we showed that for \( v \equiv 1 \) or \( 3 \pmod{6} \), there is an equitable \( k \)-edge coloring of \( K_v \) that does not admit any polychromatic \( STS(v) \), when \( k = 2, 3 \), and \( v – 2 \). In this paper, we extend the results to all feasible values of \( k \), where \( 2 \leq k \leq v – 2 \).