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Clique family inequalities
,
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 , 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.
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