  The gonality sequence $(\gamma_r)_{r\geq1}$ of a finite graph / metric graph
/ algebraic curve comprises the minimal degrees $\gamma_r$ of linear systems of
rank $r$. For the complete graph $K_d$, we show that $\gamma_r = kd - h$ if
$r<g=\frac{(d-1)(d-2)}{2}$, where $k$ and $h$ are the uniquely determined
integers such that $r = \frac{k(k+3)}{2} - h$ with $1\leq k\leq d-3$ and $0
\leq h \leq k $. This shows that the graph $K_d$ has the gonality sequence of a
smooth plane curve of degree $d$. The same result holds for the corresponding
metric graphs.

Combinatorics;Algebraic Geometry