# A note on the Chvátal-rank of clique family inequalities

Arnaud Pêcher; Annegret K. Wagler

RAIRO - Operations Research (2007)

- Volume: 41, Issue: 3, page 289-294
- ISSN: 0399-0559

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topPêcher, Arnaud, and Wagler, Annegret K.. "A note on the Chvátal-rank of clique family inequalities." RAIRO - Operations Research 41.3 (2007): 289-294. <http://eudml.org/doc/250135>.

@article{Pêcher2007,

abstract = {
Clique family inequalities
a∑v∈W xv + (a - 1)∈v∈W, xv ≤ aδ
form an intriguing class of valid inequalities
for the stable set polytopes of all graphs.
We prove firstly
that their
Chvátal-rank is at most a, which
provides an alternative proof for the validity of clique family inequalities,
involving only standard rounding arguments.
Secondly, we strengthen the upper bound further and discuss consequences
regarding the Chvátal-rank of subclasses of claw-free graphs.
},

author = {Pêcher, Arnaud, Wagler, Annegret K.},

journal = {RAIRO - Operations Research},

keywords = {Stable set polytope; Chvátal-rank; stable set polytope; Chvàtal-Rank},

language = {eng},

month = {8},

number = {3},

pages = {289-294},

publisher = {EDP Sciences},

title = {A note on the Chvátal-rank of clique family inequalities},

url = {http://eudml.org/doc/250135},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Pêcher, Arnaud

AU - Wagler, Annegret K.

TI - A note on the Chvátal-rank of clique family inequalities

JO - RAIRO - Operations Research

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 3

SP - 289

EP - 294

AB -
Clique family inequalities
a∑v∈W xv + (a - 1)∈v∈W, xv ≤ aδ
form an intriguing class of valid inequalities
for the stable set polytopes of all graphs.
We prove firstly
that their
Chvátal-rank is at most a, which
provides an alternative proof for the validity of clique family inequalities,
involving only standard rounding arguments.
Secondly, we strengthen the upper bound further and discuss consequences
regarding the Chvátal-rank of subclasses of claw-free graphs.

LA - eng

KW - Stable set polytope; Chvátal-rank; stable set polytope; Chvàtal-Rank

UR - http://eudml.org/doc/250135

ER -

## References

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- T.M. Liebling, G. Oriolo, B. Spille, and G. Stauffer, On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs. Math. Methods Oper. Res.59 (2004) 25–35 Zbl1060.90079
- G. Oriolo, On the Stable Set Polytope for Quasi-Line Graphs, Special issue on stability problems. Discrete Appl. Math.132 (2003) 185–201. Zbl1052.90108
- A. Pêcher and A. Wagler, Almost all webs are not rank-perfect. Math. Program.B105 (2006) 311–328. Zbl1083.05032
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