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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00664 |
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| _version_ | 1866914361283444736 |
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| author | Shinde, Vrushali Kadam, Lata |
| author_facet | Shinde, Vrushali Kadam, Lata |
| contents | A transversal coalition in a hypergraph $H$ is a partition of the vertex set $U$ into two subsets $U_1$ and $U_2$ such that neither $U_1$ nor $U_2$ alone intersects every hyperedge of $H$, but their union, $U_1 \cup U_2$, intersects every hyperedge in $H$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Transversal Coalition in r-Uniform Hypergraphs Shinde, Vrushali Kadam, Lata Combinatorics 05C65 A transversal coalition in a hypergraph $H$ is a partition of the vertex set $U$ into two subsets $U_1$ and $U_2$ such that neither $U_1$ nor $U_2$ alone intersects every hyperedge of $H$, but their union, $U_1 \cup U_2$, intersects every hyperedge in $H$. 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. |
| title | On the Transversal Coalition in r-Uniform Hypergraphs |
| topic | Combinatorics 05C65 |
| url | https://arxiv.org/abs/2603.00664 |