Separating the Edges of a Graph by Cycles and by Subdivisions of K4
A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) of (Formula presented.), there exists an element in (Formula presented.) that...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/484458 |
| Acceso en línea: | http://hdl.handle.net/2072/484458 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph Separating system Subdivision 51 |
| Sumario: | A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) of (Formula presented.), there exists an element in (Formula presented.) that contains (Formula presented.) but not (Formula presented.). Recently, it has been shown that every graph of order (Formula presented.) admits a separating system consisting of (Formula presented.) paths, improving the previous almost linear bound of (Formula presented.), and settling conjectures posed by Balogh, Csaba, Martin, and Pluhár and by Falgas-Ravry, Kittipassorn, Korándi, Letzter, and Narayanan. We investigate a natural generalization of these results to subdivisions of cliques, showing that every graph admits both a separating system consisting of (Formula presented.) edges and cycles and a separating system consisting of (Formula presented.) edges and subdivisions of (Formula presented.). |
|---|