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, 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.
@article{10_37236_6876,
author = {Filip Cools and Marta Panizzut},
title = {The gonality sequence of complete graphs},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/6876},
zbl = {1398.14064},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6876/}
}
TY - JOUR
AU - Filip Cools
AU - Marta Panizzut
TI - The gonality sequence of complete graphs
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6876/
DO - 10.37236/6876
ID - 10_37236_6876
ER -
%0 Journal Article
%A Filip Cools
%A Marta Panizzut
%T The gonality sequence of complete graphs
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6876/
%R 10.37236/6876
%F 10_37236_6876
Filip Cools; Marta Panizzut. The gonality sequence of complete graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6876
