Recognizing hyperelliptic graphs in polynomial time
Data Structures and Algorithms
2019-09-24 v2 Discrete Mathematics
Combinatorics
Abstract
Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1 are trees. We consider so-called "hyperelliptic graphs" (multigraphs of gonality 2) and provide a safe and complete sets of reduction rules for such multigraphs, showing that for three of the flavors of gonality, we can recognize hyperelliptic graphs in O(n log n+m) time, where n is the number of vertices and m the number of edges of the multigraph.
Cite
@article{arxiv.1706.05670,
title = {Recognizing hyperelliptic graphs in polynomial time},
author = {Jelco M. Bodewes and Hans L. Bodlaender and Gunther Cornelissen and Marieke van der Wegen},
journal= {arXiv preprint arXiv:1706.05670},
year = {2019}
}
Comments
33 pages, 8 figures