
TL;DR
This paper introduces hyperpaths, a new class of high-dimensional hypertrees analogous to paths in graph theory, and explores their properties, especially in dimension two, expanding the understanding of hypertree structures.
Contribution
It defines hyperpaths as a novel class of hypertrees, provides a family of such structures for all dimensions, and investigates their properties in dimension two.
Findings
Defined hyperpaths as high-dimensional path analogs
Constructed an infinite family of hyperpaths for each dimension
Analyzed properties of hyperpaths in dimension two
Abstract
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 -dimensional hyperpath is a -dimensional hypertree in which every -dimensional face is contained in at most faces of dimension . We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension .
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
