Gregarious Decompositions of Complete Equipartite Graphs and Related Structures

Author:

Tuza Zsolt12ORCID

Affiliation:

1. Alfréd Rényi Institute of Mathematics, Reáltanoda Str. 13-15, 1053 Budapest, Hungary

2. Faculty of Information Technology, University of Pannonia, Egyetem Str. 10, 8200 Veszprém, Hungary

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.

Funder

National Research, Development and Innovation Office, NKFIH

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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5. Akiyama, J., Kano, M., and Sakai, T. (2013). Computational Geometry and Graphs, Springer. Lecture Notes in Computer Science 8296.

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