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2010

Copositive programming motivated bounds on the stability and the chromatic numbers

10 years 1 days ago
Copositive programming motivated bounds on the stability and the chromatic numbers
The Lov´asz theta number of a graph G can be viewed as a semidefinite programming relaxation of the stability number of G. It has recently been shown that a copositive strengthening of this semidefinite program in fact equals the stability number of G. We introduce a related strengthening of the Lov´asz theta number toward the chromatic number of G, which is shown to be equal to the fractional chromatic number of G. Solving copositive programs is NP-hard. This motivates the study of tractable approximations of the copositive cone. We investigate the Parrilo hierarchy to approximate this cone and provide computational simplifications for the approximation of the chromatic number of vertex transitive graphs. We provide some computational results indicating that the Lov´asz theta number can be strengthened significantly toward the fractional chromatic number of G on some Hamming graphs.
Igor Dukanovic, Franz Rendl
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MP
Authors Igor Dukanovic, Franz Rendl
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