Abstract
In this article we study the treewidth of the display graph, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display graph is bounded if the trees are in some formal sense topologically similar. Here we further expand upon this relationship. We analyse a number of reduction rules, commonly used in the phylogenetics literature to obtain fixed parameter tractable algorithms. In some cases (the subtree reduction) the reduction rules behave similarly with respect to treewidth, while others (the cluster reduction) behave very differently, and the behaviour of the chain reduction is particularly intriguing because of its link with graph separators and forbidden minors. We also show that the gap between treewidth and Tree Bisection and Reconnect (TBR) distance can be infinitely large, and that unlike, for example, planar graphs the treewidth of the display graph can be as much as linear in its number of vertices. A number of other auxiliary results are given. We conclude with a discussion and list a number of open problems.
Original language  English 

Pages (fromto)  99117 
Number of pages  19 
Journal  Theoretical Computer Science 
Volume  731 
Early online date  18 Apr 2018 
DOIs  
Publication status  Published  30 Jun 2018 
Keywords
 Graph Theory
 Phylogenetics
 Treewidth
 Algorithmic Graph Theory
 Computational Biology
Profiles

Taoyang Wu
 School of Computing Sciences  Lecturer in Computing Sciences
 Computational Biology  Member
Person: Research Group Member, Academic, Teaching & Research