Bibliographic Details
| Title: |
On the existence of combinatorial configurations |
| Authors: |
Bras Amorós, Maria, Stokes, Klara |
| Publisher Information: |
Iniciativa Digital Politècnica |
| Publication Year: |
2011 |
| Collection: |
Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge |
| Subject Terms: |
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Graph theory, Combinatorial analysis, Bipartite graphs, Combinatorial designs and configurations, Grafs, Teoria de, Anàlisi combinatòria, Configuracions i dissenys combinatoris, Classificació AMS::05 Combinatorics::05B Designs and configurations, Classificació AMS::05 Combinatorics::05C Graph theory |
| Description: |
A (v, b, r, k) combinatorial configuration can be defined as a connected, (r, k)-biregular bipartite graph with v vertices on one side and b vertices on the other and with no cycle of length 4. Combinatorial configurations have become very important for some cryptographic applications to sensor networks and to peer-to-peer communities. Configurable tuples are those tuples (v, b, r, k) for which a (v, b, r, k) combinatorial configuration exists. It is proved in this work that the set of configurable tuples with fixed r and k has the structure of a numerical semigroup. The semigroup is completely described whenever r = 2 or r = 3. For the remaining cases some bounds are given on the multiplicity and the conductor of the numerical semigroup. This leads to some concluding results on the existence of configurable tuples. ; Peer Reviewed |
| Document Type: |
conference object |
| File Description: |
23 p.; application/pdf |
| Language: |
English |
| Relation: |
International Workshop on Optimal Networks Topologies; http://hdl.handle.net/2099/10372 |
| Availability: |
http://hdl.handle.net/2099/10372 |
| Rights: |
Open Access |
| Accession Number: |
edsbas.2FC3B20C |
| Database: |
BASE |
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