The general-coloring palette conjecture for complete graphs

Let $K_n$ be the complete graph on $n$ vertices, and let $\tau_m(n)$ denote the minimum number of colors in an edge-coloring of $K_n$ such that all triangles have distinct color palettes, where palettes are multisets of the colors on their three edges. General-coloring palette conjecture. For $n greater than or equal to 4$,

$$\tau_m(n)=n-1.$$

The preceding theorem establishes the lower bound $\tau_m(n)\geq n-1$; the conjecture asserts that this bound is attained for every $n\geq4$, extending the exceptional case $n=3$ where one color suffices.