Speaker: Sarah Loeb (Hampden-Sydney College)
Title. Tanglegram Reconstruction
Abstract. The reconstruction problem asks if we can uniquely identify a larger structure from its smaller substructures. I'll consider this problem in two contexts: rooted binary trees (a.k.a rooted phylogenetic tree shapes) and tanglegrams. For rooted binary trees, the smaller substructures are leaf-induced binary subtrees; we show such trees are reconstructable. A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that tanglegrams are reconstructable when at least one of the binary trees has that its internal vertices form a path that ends at the root.
This is joint work with Ann Clifton, \'{E}va Czabarka, Audace Dossou-Olory, Kevin Liu, Utku Okur, L\'{a}szl\'{o} Sz\'{e}kely, and Kristina Wicke.