2020/11/19 by Amir Dahari, Dahari, Amir, Nati Linial +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #cs.CC #math.CO
paper · pdf · doi:10.48550/arxiv.2011.09936
This version contains the proof of the Full Matrices section
arxiv created 2020/11/19 · openalex publication_date 2020/11/19 · arxiv updated 2020/11/20 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study Hyperpaths -- a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A d-dimensional hyperpath is a d-dimensional hypertree in which every (d-1)-dimensional face is contained in at most (d+1) faces of dimension d. We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension d=2.