Consider a complete graph $K_n$ with $n$ vertices ($n > 4$). Note that multiple spanning trees can be constructed over $K_n$. Each of these spanning trees is represented as a set of edges. The Jaccard coefficient between any two sets is defined as the ratio of the size of the intersection of the two sets to the size of the union of the two sets. Which one of the following options gives the lowest possible value for the Jaccard coefficient between any two spanning trees of $K_n$ ?

Let $T_1$ and $T_2$ be two spanning trees of the complete graph $K_n$.

The Jaccard coefficient between their edge sets is given by:

Since each spanning tree on $n$ vertices contains exactly $n - 1$ edges, two spanning trees $T_1$ and $T_2$ can be completely edge-disjoint if $|T_1 \cap T_2| = 0$.

The total number of edges in $K_n$ is $\frac{n(n - 1)}{2}$. For two edge-disjoint spanning trees to exist, the graph must have at least:

Since it is given that $n > 4$, $K_n$ always contains two edge-disjoint spanning trees $T_1$ and $T_2$.

For two edge-disjoint spanning trees:

Thus, the lowest possible value of the Jaccard coefficient is:

Hence, the correct option is (C).