Gregarious Decompositions of Complete Equipartite Graphs and Related Structures

Tuza, Zsolt (2023) Gregarious Decompositions of Complete Equipartite Graphs and Related Structures. SYMMETRY (BASEL), 15 (12). ISSN 2073-8994

Preview

Text symmetry-15-02097.pdf - Published Version Available under License Creative Commons Attribution. Download (337kB) | Preview

Abstract

In a finite mathematical structure with a given partition, a substructure is said to be gregarious if either it meets each partition class or it shares at most one element with each partition class. In this paper, we considered edge decompositions of graphs and hypergraphs into gregarious subgraphs and subhypergraphs. We mostly dealt with “complete equipartite” graphs and hypergraphs, where the vertex classes have the same size and precisely those edges or hyperedges of a fixed cardinality are present that do not contain more than one element from any class. Some related graph classes generated by product operations were also considered. The generalization to hypergraphs offers a wide open area for further research.

Actions (login required)

Edit Item