| dc.creator | Gutiérrez, Marisa | |
| dc.date | 2001 | |
| dc.date | 2022-04-11T18:36:12Z | |
| dc.date.accessioned | 2023-07-15T04:42:02Z | |
| dc.date.available | 2023-07-15T04:42:02Z | |
| dc.identifier | http://sedici.unlp.edu.ar/handle/10915/134311 | |
| dc.identifier | issn:0911-0119 | |
| dc.identifier | issn:1435-5914 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7470551 | |
| dc.description | Let P be a class of finite families of finite sets that satisfy a property P. We call ΩP the class of intersection graphs of families in P and CliqueP the class of graphs whose family of cliques is in P. We prove that a graph G is in ΩP if and only if there is a family of complete sets of G which covers all edges of G and whose dual family is in P. This result generalizes that of Gavril for circular-arc graphs and conduces those of Fulkerson-Gross, Gavril and Monma-Wei for interval graphs, chordal graphs, UV, DV and RDV graphs. Moreover, it leads to the characterization of Helly-graphs and dually chordal graphs as classes of intersection graphs. We prove that if P is closed under reductions, then CliqueP=Ω(P*∩H) (P*= Class of dual families of families in P). We find sufficient conditions for the Clique Operator, K, to map ΩP into ΩP*. These results generalize several known results for particular classes of intersection graphs. Furthermore, they lead to the Roberts-Spencer characterization for the image of K and the Bandelt-Prisner result on K-fixed classes. | |
| dc.description | Facultad de Ciencias Exactas | |
| dc.format | application/pdf | |
| dc.format | 237-244 | |
| dc.language | en | |
| dc.rights | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) | |
| dc.subject | Matemática | |
| dc.subject | Intersection Graph | |
| dc.subject | Interval Graph | |
| dc.subject | Chordal Graph | |
| dc.subject | Finite Family | |
| dc.subject | Dual Family | |
| dc.title | Intersection Graphs and the Clique Operator | |
| dc.type | Articulo | |
| dc.type | Articulo | |
