Cyclic permutations and evolutionary trees

Abstract

Given a tree T with leaf set X, there are certain ways of arranging the elements of X in a circular order so that T can be embedded in the plane and 'preserve' this ordering. We investigate some new combinatorial properties of these 'circular orderings.' We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X. © 2003 Elsevier Inc. All rights reserved.