| Title: | Conformal hypergraphs : duality and implications for the upper clique transversal problem |
|---|
| Authors: | ID Boros, Endre (Author)
ID Gurvich, Vladimir (Author)
ID Milanič, Martin (Author)
ID Uno, Yushi (Author) |
|---|
| Files: |  RAZ_Boros_Endre_2025.pdf (475,86 KB)
MD5: 16CC9114F29E2DC8B7E968A81062A3E0
 https://onlinelibrary.wiley.com/doi/full/10.1002/jgt.23238
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
IAM - Andrej Marušič Institute
|
|---|
| Abstract: | Given a hypergraph H, the dual hypergraph of H is the hypergraph of all minimal transversals of H. The dual hypergraph is always Sperner, that is, no hyperedge contains another. A special case of Sperner hypergraphs are the conformal Sperner hypergraphs, which correspond to the families of maximal cliques of graphs. All these notions play an important role in many fields of mathematics and computer science, including combinatorics, algebra, database theory, etc. In this paper we study conformality of dual hypergraphs and prove several results related to the problem of recognizing this property. In particular, we show that the problem is in co-NP and can be solved in polynomial time for hypergraphs of bounded dimension. In the special case of dimension 3, we reduce the problem to 2-Satisfiability. Our approach has an implication in algorithmic graph theory: we obtain a polynomial-time algorithm for recognizing graphs in which all minimal transversals of maximal cliques have size at most k, for any fixed k. |
|---|
| Keywords: | conformal hypergraph, dual hypergraph, hypergraph, maximal clique, upper clique transversal |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 466-480 |
|---|
| Numbering: | Vol. 109, iss. 4 |
|---|
| PID: | 20.500.12556/RUP-21787  |
|---|
| UDC: | 519.179.1 |
|---|
| ISSN on article: | 1097-0118 |
|---|
| DOI: | 10.1002/jgt.23238 |
|---|
| COBISS.SI-ID: | 230094851 |
|---|
| Publication date in RUP: | 25.09.2025 |
|---|
| Views: | 337 |
|---|
| Downloads: | 4 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
