On the gonality, treewidth, and orientable genus of a graph

Abstract

We examine connections between the gonality, treewidth, and orientable genus of a graph. Especially, we find that hyperelliptic graphs in the sense of Baker and Norine are planar. We give a notion of a bielliptic graph and show that each of these must embed into a closed orientable surface of genus one. We also find, for all $g\ge 0$, trigonal graphs of treewidth 3 and orientable genus $g$, and give analogues for graphs of higher gonality.

10 pages, comments welcome!

References in corpus (1)

• Treewidth is a lower bound on graph gonality

Cited by in corpus (1)

• Spectral Analysis of Laplacians of an Unweighted and Weighted Multidimensional Grid Graph -- Combinatorial versus Normalized and Random Walk Laplacians