Recognizing hyperelliptic graphs in polynomial time

Based on analogies between algebraic curves and graphs, Baker and Norine introduced divisorial gonality, a graph parameter for multigraphs related to treewidth, multigraph algorithms and number theory. Various equivalent definitions of the gonality of an algebraic curve translate to different notion...

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Bibliographic Details
Published in:	Theoretical computer science 2020-05, Vol.815, p.121-146
Main Authors:	Bodewes, Jelco M., Bodlaender, Hans L., Cornelissen, Gunther, van der Wegen, Marieke
Format:	Article
Language:	eng
Subjects:	Algorithms Gonality Graphs Hyperelliptic Reduction rules Treewidth
Online Access:	Get full text
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Summary:	Based on analogies between algebraic curves and graphs, Baker and Norine introduced divisorial gonality, a graph parameter for multigraphs related to treewidth, multigraph algorithms and number theory. Various equivalent definitions of the gonality of an algebraic curve translate to different notions of gonality for graphs, called stable gonality and stable divisorial gonality. We consider so-called hyperelliptic graphs (multigraphs of gonality 2, in any meaning of graph gonality) and provide a safe and complete set of reduction rules for such multigraphs. This results in an algorithm to recognize hyperelliptic graphs in time O(m+nlog⁡n), where n is the number of vertices and m the number of edges of the multigraph. A corollary is that we can decide with the same runtime whether a two-edge-connected graph G admits an involution σ such that the quotient G/〈σ〉 is a tree.
ISSN:	0304-3975 1879-2294