On the Transversal Coalition in r-Uniform Hypergraphs
Vrushali Shinde, Lata Kadam

TL;DR
This paper studies the properties of transversal coalition partitions in r-uniform hypergraphs, determining their numbers in various hypergraph classes and exploring their structural characteristics.
Contribution
It introduces the concept of transversal coalition numbers in r-uniform hypergraphs and computes these numbers for several important classes of hypergraphs.
Findings
Transversal coalition number for complete r-uniform hypergraphs
Transversal coalition number for complete bipartite r-uniform hypergraphs
Transversal coalition number for r-uniform stars, paths, and cycles
Abstract
A transversal coalition in a hypergraph is a partition of the vertex set into two subsets and such that neither nor alone intersects every hyperedge of , but their union, , intersects every hyperedge in . In this work, we investigate transversal coalition partitions in \( r \)-uniform hypergraphs. Specifically, we determine the transversal coalition number of complete \( r \)-uniform hypergraph, complete bipartite \( r \)-uniform hypergraph, \( r \)-uniform stars, and complete \( r \)-partite \( r \)-uniform hypergraph. We also investigate the transversal coalition number of \( r \)-uniform linear paths and cycles.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Game Theory and Voting Systems
