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

Abstract

In [1], we showed that for $v\equiv 1$ or $3(\mathrm{mod}6)$, 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 $2\le k\le v–2$.