*Article* **Knots and Knot-Hyperpaths in Hypergraphs**

**Saifur Rahman 1, Maitrayee Chowdhury 1, Firos A. <sup>2</sup> and Irina Cristea 3,\***


**Abstract:** This paper deals with some theoretical aspects of hypergraphs related to hyperpaths and hypertrees. In ordinary graph theory, the intersecting or adjacent edges contain exactly one vertex; however, in the case of hypergraph theory, the adjacent or intersecting hyperedges may contain more than one vertex. This fact leads to the intuitive notion of knots, i.e., a collection of explicit vertices. The key idea of this manuscript lies in the introduction of the concept of the knot, which is a subset of the intersection of some intersecting hyperedges. We define knot-hyperpaths and equivalent knot-hyperpaths and study their relationships with the algebraic space continuity and the pseudo-open character of maps. Moreover, we establish a sufficient condition under which a hypergraph is a hypertree, without using the concept of the host graph.

**Keywords:** hypergraph; hyperpath; hypertree; knot; hypercontinuity; equivalent hyperpaths
