We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequality with (a,a+1)-valued coefficients (rank facets have only coefficients 0, 1), and (ii) providing new facets of the stable set polytope with up to five different non-zero coefficients for claw-free graphs. We prove that coefficients have to be consecutive in any facet with exactly two different non-zero coefficients (assuming they are relatively prime). Last but not least, we present a complete description of the stable set polytope for graphs with stability number 2, already observed by Cook [3] and Shepherd [18].

Liebling, T., Oriolo, G., Spille, B., Stauffer, G. (2004). On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 59(1), 25-35 [10.1007/s001860300317].

On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs

ORIOLO, GIANPAOLO;
2004-01-01

Abstract

We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequality with (a,a+1)-valued coefficients (rank facets have only coefficients 0, 1), and (ii) providing new facets of the stable set polytope with up to five different non-zero coefficients for claw-free graphs. We prove that coefficients have to be consecutive in any facet with exactly two different non-zero coefficients (assuming they are relatively prime). Last but not least, we present a complete description of the stable set polytope for graphs with stability number 2, already observed by Cook [3] and Shepherd [18].
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/09 - Ricerca Operativa
English
Circulant graphs; Claw-free graphs; Clique family inequalities; Quasi-line graphs; Stable sets
Liebling, T., Oriolo, G., Spille, B., Stauffer, G. (2004). On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 59(1), 25-35 [10.1007/s001860300317].
Liebling, T; Oriolo, G; Spille, B; Stauffer, G
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/39090
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 16
social impact