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- Title
Knots and Knot-Hyperpaths in Hypergraphs.
- Authors
Rahman, Saifur; Chowdhury, Maitrayee; A., Firos; Cristea, Irina
- 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.
- Subjects
ALGEBRAIC spaces; GRAPH theory; HYPERGRAPHS; CHARTS, diagrams, etc.
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 3, p424
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10030424