2014/08/15 by R. Sean Bowman, Bowman, R. Sean, Douglas R. Heisterkamp +4
Computer Science · Mathematics · #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Rough Sets and Fuzzy Logic #Topological and Geometric Data Analysis #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.1408.4074
15 pages, 6 figures
arxiv created 2014/08/15 · openalex publication_date 2014/08/15 · arxiv updated 2014/08/19 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position we arrive at a special type of tree position we call thin, and we show that partitions arising from thin tree positions have especially nice properties. The algorithm is based the topological notion of thin position for knots and 3-manifolds and builds on the previously defined idea of a Topological Intrinsic Lexicographic Order (TILO).