Minimum proper interval graphs : Notas de Matemática, 52
A graph G is a proper interval graph if there exists a mapping r from V(G) to the class of closed intervals of the real line with the properties that for distinct vertices v and w we have r(n) ∩ r(w) 7^ 0 if and only if v and w are adjacent and neither of the intervals r(v), r(w) contain the other....
Guardado en:
| Autores principales: | , |
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| Formato: | Publicacion seriada |
| Lenguaje: | Inglés |
| Publicado: |
1993
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/170313 |
| Aporte de: |
| Sumario: | A graph G is a proper interval graph if there exists a mapping r from V(G) to the class of closed intervals of the real line with the properties that for distinct vertices v and w we have r(n) ∩ r(w) 7^ 0 if and only if v and w are adjacent and neither of the intervals r(v), r(w) contain the other. We prove that for every proper interval graph G, | V(C7)| > 2c(G) — c(7C(Gi)), where c(G) is the number of cliques of G and Λ’((7) is the clique graph of G. If the equality is verified we call G a minimum proper interval graph. The main result is that the restriction to the class of minimum proper interval graphs of clique mapping G —> A(G) is a bijection (up to isomorphism) onto the class of proper interval graphs. We find the greatest clique-closed class Σ (i.e. Α(Σ) = Σ) contained in the union of the class of connected minimum proper interval graphs and the class of complete graphs . We enumerate the minimun proper interval graphs with n vertices. |
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