2015/08/05 by Claude Laflamme, Laflamme, Claude, Maurice Pouzet +3
Computer Science · Mathematics · #06A #06B #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:06A #msc:06B
paper · pdf · doi:10.48550/arxiv.1508.01123
openalex publication_date 2015/08/05 · openalex created_date 2016/06/24 · arxiv created 2016/09/30 · arxiv updated 2016/10/03 · openalex updated_date 2026/07/28
A tree is scattered if no subdivision of the complete binary tree is a subtree. Building on results of Halin, Polat and Sabidussi, we identify four types of subtrees of a scattered tree and a function of the tree into the integers at least one of which is preserved by every embedding. With this result and a result of Tyomkyn, we prove that the tree alternative property conjecture of Bonato and Tardif holds for scattered trees and a conjecture of Tyomkin holds for locally finite scattered trees.