English

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.

Keywords

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